CN115453890B - Global nonsingular terminal sliding mode control method of gear inspection robot system - Google Patents
Global nonsingular terminal sliding mode control method of gear inspection robot system Download PDFInfo
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Abstract
A global nonsingular terminal sliding mode control method of a gear inspection robot system is based on a mathematical model of an N-joint mechanical arm of the gear inspection robot system, and a tracking error equation of a target track and an actual motion track is constructed; on the basis, an output tracking error proportional term, an output tracking error integral nonsingular terminal term and an output tracking error initial term are introduced, a finite time convergence global nonsingular terminal sliding mode surface is constructed, and the finite time convergence of a sliding stage is achieved; and the super-spiral approach law is adopted to inhibit the high-frequency vibration phenomenon, so that nonlinear high-precision control is obtained.
Description
Technical Field
The invention relates to the technical field of industrial robot control systems, in particular to a global nonsingular terminal sliding mode control method of a gear inspection robot system.
Background
The gear mainly consists of tooth surfaces, tooth circles and gear teeth, and is used as one of important transmission elements in a mechanical structure, and the machining precision of the gear can directly influence the mechanical performance. The conventional gear finishing process comprises: rough grinding, finish grinding, polishing and the like, the quality of the surface processing technology directly influences the transmission performance of the gear, and in order to effectively improve the detection efficiency of the gear, a gear inspection robot with terminal vision is usually adopted for operation. The gear inspection robot comprises an N-joint mechanical arm and a tail end vision assembly, and in order to finish multi-angle gear inspection, accurate track motion is important. However, the N-joint mechanical arm of the gear inspection robot is an N-degree-of-freedom nonlinear system, and the system has the problems of uncertainty, high nonlinearity, strong coupling and the like, and conventional control methods, such as a sliding mode controller design method based on a multi-parameter adaptive neural network disclosed in patent CN113589689a and a self-adaptive inversion integral nonsingular rapid terminal sliding mode controller design method disclosed in patent CN112241124a, cannot meet the requirement of high-precision control.
Disclosure of Invention
Aiming at the technical problem of how to effectively improve the track tracking precision of the N-degree-of-freedom gear inspection robot system, the invention provides the following technical scheme: constructing a tracking error equation based on a mathematical model of the N-joint mechanical arm of the gear inspection robot system; constructing a limited-time convergence global nonsingular terminal sliding mode surface by utilizing an output tracking error, an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term of the gear inspection robot system; based on the supercoiled approach law, designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system, and verifying stability.
A global nonsingular terminal sliding mode control method of a gear inspection robot system is characterized in that: comprises the following steps of
Step 1, constructing a tracking error equation based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system;
step 2, constructing a finite time convergence global nonsingular terminal sliding mode surface by utilizing an output tracking error, an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term of the gear inspection robot system;
and step 3, designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system based on the supercoiled approach law, and verifying stability.
Further, in step 1, the gear inspection robot system includes an image operation center, a high-power camera, and an N-joint mechanical arm.
Further, in step 1, the mathematical model of the N-joint mechanical arm of the gear inspection robot system is as follows:
wherein q (t) represents the angle of the joint of the N joint mechanical arm of the gear inspection robot system, the first order and the second order respectively represent the angular velocity and the angular acceleration, and 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×n Friction force item of N-joint mechanical arm of gear inspection robot system>External disturbance term τ d (t)∈R n×n ；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×n ；
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, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking first-order differentiation of tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is a first order derivative of e (t); />Is q * (t) first order differentiation; />Is the first derivative of q (t);
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).
Further, in step 2, the integral sliding mode surface is defined:
s(t)＝k p e(t)+k i ∫e(t)dt
wherein s (t) is the integral slip-form surface; k (k) p and ki Parameter adjusting gains of a proportion term and an integral term respectively;
based on the integral sliding mode surface, an output tracking error integral nonsingular terminal term and an output tracking error initial term are introduced, and a finite time convergence global nonsingular terminal sliding mode surface is constructed:
s(t)＝[s 1 (t)，s 2 (t)...s n (t)] T
k p ＝diag[k 1p ，k 2p ...k np ] T
k i ＝diag[k 1i ，k 2i ...k ni ] T
e(t)＝[e 1 (t)，e 2 (t)...e n (t)] T
e p/j (t)＝[e 1 p/j (t)，e 2 p/j (t)...e n p/j (t)] T
e(0)＝[e 1 (0)，e 2 (0)...e n (0)] T
wherein ,s1 (t)，s 2 (t)...s n (t) is a sub-slip plane of a finite time converging global nonsingular terminal slip plane s (t); k (k) p and ki Parameter adjustment gains of an output tracking error proportional term, an initial term and an output tracking error integral nonsingular terminal term are respectively obtained; the parameter adjusting gain p is less than j and less than 2p, and p and j are positive odd numbers;
taking first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface to obtain:
wherein ,is a first order derivative of s (t);
taking outThe preparation method comprises the following steps:
wherein ,ts Is the convergence time and c is a constant.
Further, in step 2, defining the supercoiled approximation law:
wherein a is more than 0, b is more than 0 and is the parameter adjusting gain,
further, in step 3, the first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface and the supercoiled approximation law are combined to obtain:
will be described aboveTaking primary differentiation to obtain:
further, in the step 3, the mathematical model of the N-joint mechanical arm of the gear inspection robot system is established simultaneously; tracking errors of the N joint mechanical arm of the gear inspection robot system are subjected to first-order differentiation and second-order differentiation; designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system:
the invention has the beneficial effects that:
(1) Introducing an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term, and constructing a finite time convergence global nonsingular terminal sliding mode surface to achieve finite time convergence in a sliding stage;
(2) The finite time convergence global nonsingular terminal sliding die surface consists of an output tracking error, an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term of the gear inspection robot system, so that the problem of singularity is effectively avoided, the initial stage is ensured to be fixed on the sliding die surface, and the approaching phase is eliminated;
(3) The super-spiral approach law is adopted to inhibit the high-frequency vibration phenomenon, and nonlinear high-precision control is obtained;
(4) Compared with the traditional PID control method, the method has higher adaptability.
Drawings
Fig. 1 is a schematic diagram of a control principle frame of a global nonsingular terminal sliding mode control method of a gear inspection robot system according to an embodiment of the invention.
Fig. 2 is a schematic diagram of track tracking of a target track (1) of a double-joint mechanical arm of a global nonsingular terminal sliding mode control method of a gear inspection robot system and a track tracking of a global nonsingular terminal sliding mode control method (GNTSMC) of the gear inspection robot system according to an embodiment of the present invention.
Fig. 3 is a schematic diagram of track tracking of a target track (2) of a double-joint mechanical arm of a global nonsingular terminal sliding mode control method of a gear inspection robot system and a track tracking of a global nonsingular terminal sliding mode control method (GNTSMC) of the gear inspection robot system according to an embodiment of the present invention.
Fig. 4 is a schematic diagram of track tracking of a target track (1) of a double-joint mechanical arm and a track tracking of a traditional PID control method of the global nonsingular terminal sliding mode control method of the gear inspection robot system according to the embodiment of the invention.
Fig. 5 is a schematic diagram of track tracking of a target track (2) of a double-joint mechanical arm and a track tracking of a traditional PID control method of the global nonsingular terminal sliding mode control method of the gear inspection robot system according to the embodiment of the invention.
Detailed Description
The technical scheme of the invention is further described in detail below with reference to the attached drawings.
Referring to fig. 1, for an embodiment of the present invention, a global nonsingular terminal sliding mode control method of a gear inspection robot system is provided, and the method organically unifies a mathematical model of an N-joint mechanical arm of the gear inspection robot system, a limited time convergence global nonsingular terminal sliding mode surface, and a supercoiled approach law into an N-joint mechanical arm controller u (t) of the gear inspection robot system, referring to fig. 1, a schematic diagram of a control principle frame of the global nonsingular terminal sliding mode control method of the gear inspection robot system of the present invention specifically includes:
s1: and constructing a tracking error equation based on the mathematical model of the N-joint mechanical arm of the gear inspection robot system.
The gear inspection robot 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>Gravity item G (q (t)) n×n N-joint mechanical arm friction force item of gear inspection robot systemExternal disturbance term τ d (t)∈R n×n ；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×n 。
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, and e (t) is the N-joint mechanical arm of the gear inspection robot systemIs used for tracking errors of the optical system.
Taking first-order differentiation of tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is a first order derivative of e (t); />Is q * (t) first order differentiation; />Is the first derivative of q (t).
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).
S2: and constructing a limited-time convergence global nonsingular terminal sliding mode surface by utilizing the output tracking error, the output tracking error proportion term, the output tracking error integral nonsingular terminal term and the output tracking error initial term of the gear inspection robot system.
Defining said integral slip plane:
s(t)＝k p e+k i ∫e dt
wherein s (t) is the integral slip-form surface; k (k) p and ki The parameter tuning gains of the proportional term and the integral term are respectively.
Based on the integral sliding mode surface, an output tracking error integral nonsingular terminal term and an output tracking error initial term are introduced, and a finite time convergence global nonsingular terminal sliding mode surface is constructed:
s(t)＝[s 1 (t)，s 2 (t)...s n (t)] T
k p ＝diag[k 1p ，k 2p ...k np ] T
k i ＝diag[k 1i ，k 2i ...k ni ] T
e(t)＝[e 1 (t)，e 2 (t)...e n (t)] T
e p/j (t)＝[e 1 p/j (t)，e 2 p/j (t)...e n p/j (t)] T
e(0)＝[e 1 (0)，e 2 (0)...e n (0)] T
wherein ,s1 (t)，s 2 (t)...s n (t) is a sub-slip plane of a finite time converging global nonsingular terminal slip plane s (t); k (k) p and ki Parameter adjustment gains of an output tracking error proportional term, an initial term and an output tracking error integral nonsingular terminal term are respectively obtained; the tuning gain p < j < 2p and p, j are positive odd numbers.
Taking first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface to obtain:
wherein ,is a first order derivative of s (t).
Taking outThe preparation method comprises the following steps:
wherein ,ts Is the convergence time and c is any constant.
S3: based on the supercoiled approach law, designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system, and verifying stability.
Defining the supercoiled approximation law:
wherein a is more than 0, b is more than 0 and is the parameter adjusting gain,
and combining the first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface and the supercoiled approximation law to obtain:
will be described aboveTaking primary differentiation to obtain:
the mathematical model of the N joint mechanical arm of the gear inspection robot system is established simultaneously; tracking errors of the N joint mechanical arm of the gear inspection robot system are subjected to first-order differentiation and second-order differentiation; designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system:
to demonstrate the stability of the controller, the Lyapunov function was increased as:
where V is the Lyapunov function.
Wherein a is large enough to ensure
Referring to fig. 1, which is a schematic diagram of a control principle frame of a global nonsingular terminal sliding mode control method of a gear inspection robot system, the method of the invention is further described, and a main control diagram process is as follows: firstly, importing a target track of an N-joint mechanical arm of a gear inspection robot system; secondly, based on a tracking error equation of a target track and an actual motion track, combining an output tracking error proportional term, an output tracking error integral nonsingular terminal term and an output tracking error initial term to construct a finite time convergence global nonsingular terminal sliding mode surface; finally, designing a gear inspection robot system N-joint mechanical arm controller tau (t) through a supercoiled approach law.
Preferably, the embodiment also needs to explain that, compared with the prior art, the invention discloses a global nonsingular terminal sliding mode control method of a gear inspection robot system, which aims at realizing tracking on the target track of an N-joint mechanical arm of the gear inspection robot system by adopting a limited-time convergent global nonsingular terminal sliding mode and then achieving the purpose of inhibiting high-frequency switching vibration by using a supercoiled approach law. The limited time convergence global nonsingular terminal sliding mode surface consists of an output tracking error of the gear inspection robot system, an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term, so that the problem of singularity is effectively avoided, the initial stage is ensured to be fixed on the sliding mode surface, and the approach phase is eliminated.
Referring to fig. 2 to 5, in another embodiment of the present invention, which is different from the first embodiment, a test verification of a global non-singular terminal sliding mode control method of a gear inspection robot system is provided, including:
in order to verify and explain the technical effects adopted in the method, in the embodiment, a comparison test is carried out by using a traditional PID control method and the method of the invention, and the test results are compared by using a scientific demonstration means to verify the real effects of the method.
In order to verify that the method has higher self-adaptability compared with the traditional PID control method, the method adopts a global nonsingular terminal sliding mode control method (GNTSMC) of a gear inspection robot system to track target tracks (1) and (2) of a double-joint mechanical arm, and performs track tracking comparison test with the traditional PID control method.
Test environment: referring to fig. 1, a gear inspection robot system N-joint mechanical arm is operated on a simulation platform to simulate and track target tracks (1) and (2) of a double-joint mechanical arm, and a global non-singular terminal sliding mode control method (GNTSMC) and a traditional PID control method of the gear inspection robot system are used for testing and obtaining 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, and a track tracking comparison test result is obtained through calculation.
Referring to fig. 2 to 5, track tracking curves are compared between a global nonsingular terminal sliding mode control method (GNTSMC) and a traditional PID control method of the gear inspection robot system according to the present invention by using target tracks (1) and (2) of the double-joint mechanical arm.
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 =3kg, connecting rod2 distance l to joint 2 ce =1m, connecting rod 2 moment of inertia I 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。
q(t)＝[q 1 (t) q 2 (t)] T
τ(t)＝[τ 1 (t) τ 2 (t)] T
wherein ,ε＝m e l 1 l ce cos(δ e )，η＝m e l 1 l ce sin(δ e )。
e(t)＝q * (t)-q(t),
α=6.73, β=3.4, ε=3, η=0 is calculated.
Referring to fig. 2 to 5, k 1p ＝20000000，k 1i ＝10000，p 1 ＝3，q 1 ＝5，a 1 ＝50，b 1 ＝0.05，k 2p ＝20000000000，k 2i ＝1，p 2 ＝5，q 2 ＝7，a 2 ＝0.5，b 2 The parameters of the conventional PID control method for the target trajectories (1) and (2) of the double-joint mechanical arm are 20, 10,5 and 5, 10, respectively. The global nonsingular terminal sliding mode control method (GNTSMC) of the gear inspection robot system can completely track target tracks (1) and (2) of the double-joint mechanical arm, has better dynamic performance, high stability and small system error, and can not effectively track the target tracks (1) and (2) of the double-joint mechanical arm within 10 seconds of a test by using a traditional PID control method for comparison, and the tracking error of the system of the PID control method is maximum when the target track (1) of the double-joint mechanical arm is tracked, so that the traditional PID control method is not suitable for the gear inspection robot system with high nonlinear strong coupling.
In summary, the global nonsingular terminal sliding mode control method of the gear inspection robot system has great advantages in control precision, robustness and self-adaption, and benefits from the finite time convergence global nonsingular terminal sliding mode surface and the supercoiled approach law which are formed by the output tracking error proportional term, the output tracking error integral nonsingular terminal term and the output tracking error initial term.
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. The computer program can be applied to the input data to perform the functions described herein, thereby converting 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 (2)
1. A global nonsingular terminal sliding mode control method of a gear inspection robot system is characterized in that: comprises the following steps of
Step 1, constructing a tracking error equation based on a mathematical model of an N-joint mechanical arm of a gear inspection robot system;
in step 1, the mathematical model of the N-joint mechanical arm of the gear inspection robot system is as follows:
wherein q (t) represents the angle of the joint of the N joint mechanical arm of the gear inspection robot system, the first order and the second order respectively represent the angular velocity and the angular acceleration, and 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×n N-joint mechanical arm friction force of gear inspection robot systemItem->External disturbance term τ d (t)∈R n×n ；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×n ；
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, and e (t) is a tracking error of the N-joint mechanical arm of the gear inspection robot system;
taking first-order differentiation of tracking error of the N-joint mechanical arm of the gear inspection robot system to obtain:
wherein ,is a first order derivative of e (t); />Is q * (t) first order differentiation; />Is the first derivative of q (t);
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);
in step 2, an integral slip plane is defined:
s(t)＝k p e(t)+k i ∫e(t)dt
wherein s (t) is the integral slip-form surface; k (k) p and ki Parameter adjusting gains of a proportion term and an integral term respectively;
based on the integral sliding mode surface, an output tracking error integral nonsingular terminal term and an output tracking error initial term are introduced, and a finite time convergence global nonsingular terminal sliding mode surface is constructed:
s(t)＝[s 1 (t)，s 2 (t)…s n (t)] T
k p ＝diag[k 1p ，k 2p …k np ] T
k i ＝diag[k 1i ，k 2i …k ni ] T
e(t)＝[e 1 (t)，e 2 (t)...e n (t)] T
e p/j (t)＝[e 1 p/j (t)，e 2 p/j (t)…e n p/j (t)] T
e(0)＝[e 1 (0)，e 2 (0)…e n (0)] T
wherein ,s1 (t)，s 2 (t)…s n (t) is a sub-slip plane of a finite time converging global nonsingular terminal slip plane s (t); k (k) p and ki Parameter adjustment gains of an output tracking error proportional term, an initial term and an output tracking error integral nonsingular terminal term are respectively obtained; parameter adjusting gain p<j<2p and j are positive odd numbers;
taking first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface to obtain:
wherein ,is a first order derivative of s (t);
taking outThe preparation method comprises the following steps:
wherein ,ts Is the convergence time, c is a constant;
step 2, constructing a finite time convergence global nonsingular terminal sliding mode surface by utilizing an output tracking error, an output tracking error proportion term, an output tracking error integral nonsingular terminal term and an output tracking error initial term of the gear inspection robot system;
in step 2, a supercoiled approximation law is defined:
wherein a is>0、b>0 and is the gain of the tuning reference,
in step 3, the first-order differentiation of the limited-time convergence global nonsingular terminal sliding mode surface and the supercoiled approximation law are combined to obtain:
will be described aboveTaking primary differentiation to obtain:
step 3, designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system based on the supercoiled approach law, and verifying stability;
in the step 3, the mathematical model of the N joint mechanical arm of the gear inspection robot system is established simultaneously; tracking errors of the N joint mechanical arm of the gear inspection robot system are subjected to first-order differentiation and second-order differentiation; designing an N-joint mechanical arm controller tau (t) of the gear inspection robot system:
2. the global nonsingular terminal sliding mode control method of the gear inspection robot system according to claim 1, which is characterized in that: in step 1, the gear inspection robot system comprises an image operation center, a high-power camera and an N-joint mechanical arm.
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| CN107942684A (en) * | 2017-12-26 | 2018-04-20 | 电子科技大学 | Mechanical arm trace tracking method based on the adaptive non-singular terminal sliding formwork of fractional order |
| CN114815624A (en) * | 2022-05-25 | 2022-07-29 | 国网黑龙江省电力有限公司绥化供电公司 | Sliding mode trajectory tracking control method of multi-degree-of-freedom robot system |
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| CN107942684A (en) * | 2017-12-26 | 2018-04-20 | 电子科技大学 | Mechanical arm trace tracking method based on the adaptive non-singular terminal sliding formwork of fractional order |
| CN114815624A (en) * | 2022-05-25 | 2022-07-29 | 国网黑龙江省电力有限公司绥化供电公司 | Sliding mode trajectory tracking control method of multi-degree-of-freedom robot system |
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