Integral terminal sliding mode trajectory tracking control method based on radial basis function neural network

Abstract

The invention discloses an integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network. The method comprises the following steps: constructing an impedance control model based on a dynamic model of a six-degree-of-freedom industrial robot; designing robot grinding force control logic based on an impedance control model; designing a finite time trajectory tracking controller based on the robot dynamic model; designing an integral terminal sliding mode trajectory tracking controller based on an interference approximation method of a radial basis function neural network; and performing numerical simulation through a six-degree-of-freedom robot, and verifying the performance of the integral terminal sliding mode trajectory tracking controller. Aiming at the interaction force control problem of the industrial robot grinding system, the invention designs a novel impedance-based finite time force control algorithm so as to improve the dynamic performance of the industrial robot grinding system. Compared with the existing algorithm, the RBF + ITSMC algorithm provided by the invention has better performance in the aspects of interaction tracking speed and tracking precision, and has better anti-interference capability.

Description

Technical Field

[0001] The present invention belongs to the technical field of manipulator control, and specifically relates to an integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network. Background Technique

[0002] In recent years, many scholars have studied force / position control algorithms and published a large number of results. In practical applications, due to its simplicity, linear methods such as PID control are favored. Due to relying on the system linearization model, linear control methods have poor robustness when dealing with complex situations. In the early stage of research, in order to achieve flexible control of robot manipulators, impedance control algorithms were proposed. However, the strong coupling, uncertainty, and external environmental interference of robots make it challenging to ensure the robustness of these control methods in practical applications. In addition, in order to improve the performance of control algorithms, researchers have introduced various nonlinear control strategies. To solve the dynamic force tracking problem, an adaptive control method based on real-time modification of impedance model parameters was proposed. In some technologies, fuzzy control methods were used to achieve flexible control of robot arms and showed excellent performance in dealing with system uncertainty and external interference.

[0003] However, the above algorithms are asymptotic stability control algorithms and face the problem of not being able to converge to the equilibrium point within a finite time. In contrast, finite-time control systems can not only reach the convergence state within a finite time but also exhibit better anti-interference performance. Therefore, designing a control strategy with finite-time convergence characteristics is crucial for achieving smooth control of robot manipulators. As is well known, the sliding mode control method does not require an accurate system model and improves the system response speed, so it is convenient for the control of complex systems. In sliding mode control, the system quickly converges from the initial state to the sliding surface and then slides to reach the equilibrium point. However, there are mismatched interferences in various engineering applications, which pose a huge challenge in the design stage of sliding mode controllers.

[0004] To improve the robustness of sliding mode control in an uncertain environment, some scholars introduced an integral term when designing the sliding surface to eliminate the sliding mode reaching stage. It has been proven that the integral sliding mode control algorithm (ISMC) exhibits superior anti-interference performance. In addition, to improve the convergence speed of the system, terminal sliding mode control strategies are often used. It should be noted that terminal sliding mode control can converge within a finite time but may lead to singularity problems. In view of these points, the present invention proposes a scheme that combines the above two control theories, thus developing an integral terminal sliding mode control algorithm (ITSMC). This strategy not only achieves the convergence of the system within a finite time but also demonstrates excellent anti-interference performance while successfully avoiding singularity problems. Summary of the Invention

[0005] In view of the problem of interactive force control in the grinding system of industrial robots, a novel impedance-based finite-time force control algorithm is designed and applied to improve the dynamic performance of the grinding system of industrial robots. First, based on the impedance model, an interactive force control scheme for the grinding system is designed. Second, according to the dynamic characteristics of the robot, a finite-time control algorithm is designed. Rigorous theoretical analysis ensures that the closed-loop system has finite-time stability in the absence of interference. Third, in order to improve the anti-interference ability of the system, a disturbance approximation method based on the radial basis function (RBF) is adopted. Based on this result, a finite-time controller improved by integral terminal sliding mode is designed. Finally, the numerical simulation results verify the correctness of the theory.

[0006] To solve the above technical problems, a technical solution adopted by the present invention is:

[0007] An integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network, comprising the following steps:

[0008] Step 1: Construct an impedance control model based on the dynamic model of a six-degree-of-freedom industrial robot;

[0009] Step 2: Design the robot grinding force control logic based on the impedance control model;

[0010] Step 3: Design a finite-time trajectory tracking controller based on the robot dynamic model;

[0011] Step 4: Design an integral terminal sliding mode trajectory tracking controller based on the disturbance approximation method of the radial basis function neural network;

[0012] Step 5: Conduct numerical simulation through a six-degree-of-freedom robot to verify the performance of the integral terminal sliding mode trajectory tracking controller.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0014] 1. Based on the impedance model, the present invention designs an interactive force control scheme for the grinding system. According to the dynamic characteristics of the robot, a finite-time control algorithm is designed. Rigorous theoretical analysis ensures that the closed-loop system has finite-time stability in the absence of interference. In order to improve the anti-interference ability of the system, a disturbance approximation method based on the radial basis function (RBF) is adopted. Based on this result, a finite-time controller improved by integral terminal sliding mode is designed, and the numerical simulation results verify the correctness of the theory.

[0015] 2. In view of the problem of interactive force control in the industrial robot grinding system, the present invention designs and applies a novel impedance-based finite-time force control algorithm to improve the dynamic performance of the industrial robot grinding system. Compared with the existing FTC and PD algorithms, the RBF+ITSMC algorithm proposed by the present invention shows better performance in terms of interactive force tracking speed and tracking accuracy, and also demonstrates more excellent anti-interference ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 FIG. is a schematic structural diagram of a robot grinding system based on force feedback;

[0017] Figure 2 FIG. is a schematic block diagram of impedance-based robot force control;

[0018] Figure 3 FIG. is a schematic diagram of the process of disturbance approximation based on radial basis function;

[0019] Figure 4 FIG. is a constant interactive force tracking curve under the condition of no interference;

[0020] Figure 5 FIG. is a time-varying interactive force tracking curve under the condition of no interference;

[0021] Figure 6 FIG. is a time-varying interactive force tracking error curve under the condition of no interference;

[0022] Figure 7 FIG. is a position tracking curve in the X-axis and Y-axis directions under the condition of no interference;

[0023] Figure 8 FIG. is a constant interactive force tracking curve under the condition of existing interference;

[0024] Figure 9 FIG. is the disturbance estimation performance based on radial basis function, where the parts (a)-(f) correspond to the 1st to 6th joints of a six-degree-of-freedom robot in sequence;

[0025] Figure 10 FIG. is the robot joint tracking error curve under the condition of existing interference, where the parts (a)-(f) correspond to the 1st to 6th joints of a six-degree-of-freedom robot in sequence;

[0026] Figure 11 FIG. is a time-varying interactive force tracking curve under the condition of existing interference;

[0027] Figure 12 FIG. is a time-varying interactive force tracking error curve under the condition of existing interference;

[0028] Figure 13 FIG. is a position tracking curve in the X-axis and Y-axis directions under the condition of existing interference. Detailed Implementation Modes

[0029] The following elaborates on the preferred embodiments of the present invention in conjunction with the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more definite definition of the protection scope of the present invention.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which this invention belongs. The terms used in the specification of the present invention are only for the purpose of describing specific embodiments and are not intended to limit the present invention. The term "or / and" used herein includes any and all combinations of one or more of the related listed items.

[0031] The structural schematic diagram of the robot grinding system based on force feedback is as Figure 1 shown, mainly including an industrial robot 1, a grinding tool 4, a force sensor 3, and a workpiece 2. In the grinding task, the grinding tool 4 needs to move along a predetermined grinding trajectory 5 while maintaining high-precision force tracking in the force output direction.

[0032] The present invention provides an integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network, including the following steps:

[0033] Step 1: Construct an impedance control model based on the dynamic model of a six-degree-of-freedom industrial robot;

[0034] Step 2: Design a robot grinding force control logic based on the impedance control model;

[0035] Step 3: Design a finite-time trajectory tracking controller based on the robot dynamic model;

[0036] Step 4: Design an integral terminal sliding mode trajectory tracking controller based on the interference approximation method of a radial basis function neural network;

[0037] Step 5: Perform numerical simulation through a six-degree-of-freedom robot to verify the performance of the integral terminal sliding mode trajectory tracking controller.

[0038] The specific process is as follows:

[0039] Generally, the dynamic equation of a six-degree-of-freedom industrial robot is:

[0040]

[0041] Wherein respectively represent the angle, angular velocity, and angular acceleration of the robot, τ ∈ R 6×1 is the joint torque vector, τ f ∈ R 6×1is the disturbance torque vector, D(q) ∈ R 6×6 is the inertia matrix, G(q) ∈ R 6×1 is the gravity vector, is the centripetal and Coriolis force vector, is the robotic joint friction vector. The frictions of the robot can usually be described as follows:

[0042]

[0043] where, f c > 0 is the Coulomb friction coefficient, f v > 0 is the viscous friction coefficient, f b is the friction offset value, and sgn(·) is the sign function. For the robotic system, D(q), and G(q) are all smooth. It can be known from the existing literature that the matrix D(q) is positive definite and symmetric, while the matrix is skew-symmetric. These properties are helpful in the controller design.

[0044] Define For a vector For the sake of description, denote it as

[0045] (Homogeneous space) For e j > 0, j = 1, …, k, define a vector (e 1 , …, e k ) ∈ R k . For a vector space

[0046]

[0047] If For Ψ > -min{e j , j = 1, …, k} is satisfied, then it can be said that for the vector (e 1 , …, e k ), the vector function has the homogeneous degree Ψ ∈ R. Meanwhile, the above vector space (3) is called the homogeneous space.

[0048] Consider a perturbed vector space:

[0049]

[0050] where, where is a nominal vector space, and the perturbed vector space satisfies the condition If the nominal vector space for (e 1 , …, ek ) has a homogeneous degree Ψ < 0 and has an asymptotically stable equilibrium point Then the equilibrium point also exhibits finite-time stability. Additionally, if the perturbation vector space satisfies the condition

[0051]

[0052] Then the origin represents a locally stable equilibrium point with finite-time stability within the system.

[0053] Next, the main objective is to develop a high-precision force and position control algorithm such that the robotic grinding system can simultaneously track a predefined working trajectory and follow a predefined interaction force.

[0054] Force control strategy through impedance control:

[0055] For the workpiece to be ground, a predefined trajectory is generated according to the grinding requirements Then, an impedance-based force control algorithm is adopted to design a high-precision force / position control algorithm, and its control block diagram is as Figure 2 shown.

[0056] Specifically, the impedance model is as follows:

[0057]

[0058] where represents the desired trajectory of the robot after correction through impedance modeling, and L, B, K ∈ R 6×6 is a positive definite diagonal matrix, and F int represents the interaction force between the grinding tool and the environment (workpiece) measured by the force sensor, while F d represents the desired interaction force.

[0059] In the robot base coordinate system, it is assumed that the desired interaction force only exists in the Z-axis direction, and there is no desired interaction force in the X-axis and Y-axis directions. Therefore, after the control process shown in Figure 2 the predefined trajectories in the X-axis and Y-axis directions remain unchanged, that is, x d (t) = x p (t), y d (t) = y p (t). However, the trajectory in the Z-axis direction will be adjusted in real time according to the measured interaction force. Therefore, a high-performance composite disturbance rejection controller needs to be designed so that the robot can track the desired position.

[0060] Taking the z direction as an example, the control performance of the impedance-based interaction force control method is analyzed.

[0061] Assume that the desired interaction force only exists in the Z-axis direction and there is no desired interaction force in the X-axis and Y-axis directions. Then x d (t) = x p (t), y d (t) = y p (t). After separately extracting and rewriting the data corresponding to the Z-axis direction in the above impedance model (6), we get:

[0062]

[0063] Assume that the environment (workpiece) is equivalent to a linear spring, that is

[0064] f int = k e (z e - z d ), z d < z e ; (8)

[0065] where z e is the environment position, that is, the position of the workpiece, z d is the expected position in the Z-axis direction, and k e is the elastic coefficient. Define f e as the interaction force tracking error. The interaction force tracking error f e is:

[0066] f e = f int - f d = k e (z e - z d ) - f d ; (9)

[0067] Then

[0068]

[0069] Considering the simplest case of planar interactive force polishing, z p , z e , f d are all constants. Under this condition, are all zero. Substituting (10) into (7) gives

[0070]

[0071] Then

[0072]

[0073] According to Equation (12), when and only when , f e= 0 holds. When this condition is not satisfied, the interaction force control based on the impedance method will not be able to make the interaction force tracking error zero.

[0074] Design of a finite-time trajectory tracking controller:

[0075] For the robot grinding process, under the condition that the robot running speed is required to be kept at a slow level, it can be assumed that the desired speed remains unchanged, that is Define the tracking error η 1 = q - q d , q d and represent the desired angle and desired angular velocity of the robot respectively, and the following error dynamic system is obtained:

[0076]

[0077] For the sake of convenience of expression, D, C, and G are used as abbreviations for D(q), and G(q) respectively in the following. Next, the main goal is to design a disturbance rejection control algorithm to achieve η 1 → 0, η 2 → 0 within a finite time.

[0078] Design of a finite-time trajectory tracking controller without disturbance:

[0079] For the robot dynamic system (1) without disturbance, that is τ f ≡ 0, assume that the trajectory tracking controller is selected as:

[0080]

[0081] where, 0 < α 1 < 1, α 2 = 2α 1 / (1 + α 1 ), v 1 > 0, v 2 > 0, and it can accurately track the desired path within a finite time.

[0082] The proof is as follows:

[0083] Substitute equation (14) into equation (13), and the following robot position error dynamic system can be obtained:

[0084]

[0085] Step 1: Prove the global asymptotic stability;

[0086] For the above closed-loop system (15), select the Lyapunov function as follows:

[0087]

[0088] and along the closed-loop system (15) for W 1 Taking the derivative gives

[0089]

[0090] and

[0091]

[0092] Thus

[0093]

[0094] Using LaSalles' invariance principle, it can be concluded that the origin of the system (η 1 , η 2 ) = (0, 0) is globally asymptotically stable, which means that as t → ∞, (η 1 , η 2 ) → (0, 0).

[0095] Step 2. Prove local finite-time stability;

[0096] In this step, it will be shown that the closed-loop system (15) is locally finite-time stable, and the aforementioned lemma on local stable equilibrium points for finite-time stability is applied. The closed-loop system (15) can be reformulated as:

[0097]

[0098] where

[0099]

[0100] First, we show that the nominal system in equation (20), i.e.,

[0101]

[0102] is globally asymptotically stable and has a negative homogeneous degree. Choose the Lyapunov function as follows:

[0103]

[0104] Similar to equation (17), through equation (22), I obtain the derivative of W 2 , i.e.,

[0105]

[0106] Through the previous processing procedure, according to Equation (24), it can be concluded that the nominal system (22) achieves asymptotic stability. On the contrary, according to the aforementioned definition, the nominal system (22) exhibits a homogeneous degree Ψ = (α 1 , e 1 , e 1 , e 1 , e 1 , e 1 , e 2 , e 2 , e 2 , e 2 , e 2 , e 2 ) with respect to the dilation (e 1 - 1) / 2 < 0, where e 1 = 1, e 2 = (1 + α 1 ) / 2.

[0107] Secondly, for any (η 1 , η 2 ) ≠ 0, Equation (22) satisfies the condition

[0108] Represent a continuously differentiable function as

[0109] g(η 1 ) = D -1 (η 1 + q d ); (25)

[0110] Using the mean value inequality, we can obtain

[0111]

[0112] where O(·) represents the corresponding infinitesimal. Therefore, for any (η 1 , η 2 ) ≠ 0,

[0113]

[0114] Since Ψ = (α 1 - 1) / 2, e 1 = 1, and e 2 = (1 + α 1 ) / 2, we get:

[0115] e 1 α 1 - e 2 - Ψ = 0; (28)

[0116] Substitute this equation into Equation (27) to obtain:

[0117]

[0118] According to the foregoing lemma, it can be inferred that the closed-loop system (15) exhibits local finite-time stability. Therefore, combining the findings of the previous two steps, it is concluded that the closed-loop system (15) achieves global finite-time stability, which means that (η 1 , η 2 ) tends to zero in finite time.

[0119] Meanwhile, if α 1 = α 2 = 1, the finite-time trajectory tracking control algorithm will converge to the following control algorithm:

[0120]

[0121] This is regarded as a PD controller based on dynamic compensation. This can be regarded as a PD controller based on dynamic compensation (hereinafter referred to as PD for short). Under this controller, the closed-loop system is asymptotically stable. In the subsequent simulation section, it will be juxtaposed with the proposed trajectory tracking control algorithm.

[0122] Design of a finite-time trajectory tracking controller under the presence of disturbances: In this embodiment, the challenge of tracking the trajectory of an industrial robot is addressed, and disturbance factors such as unmodeled errors and external disturbances are considered. By integrating the integral sliding mode control method and neural networks, an improved finite-time trajectory tracking controller is developed, which can completely eliminate disturbances.

[0123] To handle the external disturbance τ f (t), a radial basis function (RBF) neural network is applied to estimate it, and the radial basis function is expressed as:

[0124]

[0125] where c j is the radial basis function data center of the j-th neuron in the hidden layer, b j is the radial basis function width in the same neuron, and m is the number of terms of the input neurons;

[0126] Assume that there exists a positive constant F such that ‖τ f (t)‖ ≤ F, and a weight matrix Y

[0127] τ f (·) = Y T h d (u) + ε; (32)

[0128] where, is the input of the neural network, and ε is the bounded neural network approximation error. is a positive constant;

[0129] The output of the neural network is:

[0130]

[0131] where, is the estimated value of the weight matrix Y;

[0132] The perturbation approximation error is expressed as

[0133]

[0134] Since h d (u) and the weight matrix E are bounded, it is inferred that e f is also bounded, that is is a positive constant.

[0135] Next, an improved finite-time trajectory tracking controller is developed through the integral terminal sliding mode control (ITSMC) algorithm based on the RBF neural network, that is, the trajectory tracking controller based on the radial basis function integral terminal sliding mode control (RBF+ITSMC).

[0136] The design of the trajectory tracking controller based on the radial basis function integral terminal sliding mode is as follows:

[0137]

[0138] where,

[0139]

[0140] Under the conditions of 0 < α 1 < 1, α 2 = 2α 1 / (1 + α 1 ), v 1 > 0, v 2 > 0, the desired trajectory can be tracked within a finite time span.

[0141] The proof is as follows:

[0142] Substituting the control algorithm (35) into the error dynamic system (13) gives

[0143]

[0144] Following the principles of the sliding mode control theory, the demonstration process is divided into two stages.

[0145] Stage 1: The reaching stage of s.

[0146] First, it is proved that the sliding mode state variable s converges to the sliding mode surface s = 0 within a finite time and remains on this surface indefinitely. The Lyapunov function is constructed as follows:

[0147]

[0148] And the derivative of W 2 is derived as:

[0149]

[0150] Utilizing the symmetric property of matrix D and Equation (38), we have

[0151]

[0152] where f (·) represents the minimum value function, that is f (x(t)) = min(x(t)).

[0153] Combining Equation (39) and Equation (40), we can obtain

[0154]

[0155] Then

[0156]

[0157] According to the existing literature records and the above lemma, it can be concluded that the sliding mode surface s = 0 is reachable within a finite time span and can be maintained permanently.

[0158] Second stage: the sliding stage of s.

[0159] Based on the results of the first stage, after reaching the stage, we have

[0160] s ≡ 0; (43) According to Equation (36), we have

[0161]

[0162] According to the foregoing assumptions and theorems, it can be inferred that within a finite time, q → q d ,

[0163] Numerical simulation: In this embodiment, a six-degree-of-freedom (6-DOF) robot is used for numerical simulation to verify the theoretical correctness. To achieve robotic grinding, the following three control algorithms are used: ① Proportional-Differential (PD) controller, ② Finite-Time Controller (FTC), and ③ Radial Basis Function-based Integral Terminal Sliding Mode Controller (RBF+ITSMC). Based on the trial-and-error method, the gains of these three control algorithms are selected as shown in Table 1.

[0164] Table 1 Gains of the Three Control Algorithms

[0165]

[0166] In the simulation, the desired trajectory of the robot in the XY plane is set as a circular trajectory centered at (0.18, 0.18 m) with a radius of R = 0.01 m. Meanwhile, in the Z direction, the desired interaction force needs to be tracked. Next, the simulation verification is mainly carried out for two cases of constant interaction force and time-varying interaction force, as well as the presence or absence of external disturbances.

[0167] Case 1: Without interference;

[0168] In this case, it is assumed that there is no interference in the robot system, i.e., τ f = 0. The following simulations are divided into two types, namely constant interaction force and time-varying interaction force.

[0169] 1) Constant interaction force. Set the desired contact force as As Figure 4 shown, the force tracking curves of the three algorithms are presented. Define the convergence criterion for the interaction force tracking as |f(t) - f d (t)| < 0.1 N. The convergence times of the interaction force tracking are given in Table 2. Based on the above results, it is concluded that compared with the PD algorithm, RBF+ITSMC and FTC provide a faster tracking rate for the interaction force.

[0170] Table 2 Comparison of Convergence Times for Constant Interaction Force Tracking without Disturbance (s)

[0171]

[0172] 2) Time-varying interaction force. Set the desired interaction force as f d (t) = (10 + 10sin(t)) N. The force tracking control response curve is as Figure 5 shown, and the interaction force tracking error is as Figure 6 shown. Obviously, compared with the PD algorithm, the RBF+ITSMC and FTC algorithms exhibit smaller steady-state errors. In addition, the position tracking results along the X and Y axes as Figure 7 shown also confirm the above conclusion.

[0173] Case 2: In the presence of interference;

[0174] In this part, the disturbing torque τ f,i = 2(7 - i)sin(2t) Nm is added to the i-th joint control channel of a six-degree-of-freedom (6-DOF) robot, where i = 1, 2, …, 6. Similarly, the following simulations are also divided into two types, namely constant interaction force and time-varying interaction force.

[0175] 1) Constant interaction force. The desired constant interaction force f d is set as described above, and the interaction force tracking curve is as Figure 8 shown. To mitigate the impact of interference on the dynamic system, a method based on radial basis function (RBF) is adopted to provide an approximate estimate of the interference, thereby eliminating them. The results of interference estimation are given in Figure 9 . It can be seen that the RBF-based method can provide effective interference estimation. In addition, Figure 10 the robot joint tracking errors are given. It can be seen that in the presence of interference, the RBF+ITSMC algorithm proposed in the present invention demonstrates superior interference suppression ability compared with the FTC and PD algorithms.

[0176] 2) Time-varying interaction force. Similarly, the same time-varying desired interaction force f d (t) is selected, and the interaction force tracking curve and tracking errors are shown in Figure 11 and Figure 12 respectively. In addition, the position tracking of the X-axis and Y-axis is given in Figure 13 . In Table 3, we provide the steady-state errors of the constant interaction force and time-varying interaction force when the external interference affects the system. All the above results demonstrate the excellent interference suppression ability of the RBF+ITSMC algorithm.

[0177] Table 3 Comparison of steady-state errors of interaction force tracking in the presence of interference (N)

[0178]

[0179] In summary, it can be concluded that compared with the FTC and PD algorithms, the RBF+ITSMC algorithm proposed in the present invention performs better in terms of interaction force tracking speed and tracking accuracy, and also demonstrates superior anti-interference ability.

[0180] The technical features of the above-described embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0181] The above are only embodiments of the present invention, and do not thus limit the patent scope of the present invention. Any equivalent structural or equivalent process transformations made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. An integral terminal sliding mode trajectory tracking control method based on radial basis function neural network, characterized in that: The following steps are involved: Step 1: construct an impedance control model based on the dynamic model of a six-degree-of-freedom industrial robot; Step 2: Design the robot grinding force control logic based on the impedance control model; Step 3: Design a finite-time trajectory tracking controller based on the robot dynamic model; Step 4: Design an integral terminal sliding mode trajectory tracking controller based on the disturbance approximation method of radial basis function neural network; Step 5: Perform numerical simulation on a robot with six degrees of freedom to verify the performance of the integral terminal sliding mode trajectory tracking controller.

2. The integral terminal sliding mode trajectory tracking control method based on radial basis function neural network according to claim 1 is characterized in that: The specific process of step 1 is as follows: The dynamic equation of a six-degree-of-freedom industrial robot is: in Respectively represent the angle, velocity and acceleration of the robot, τ∈R 6×1 is the joint torque vector, τ f ∈R 6×1 is the disturbance torque vector, D(q)∈R 6×6 is the inertia matrix, G(q)∈R 6×1 is the gravity vector, are the centripetal and Coriolis force vectors, is the robot joint friction vector, and the robot friction force is described as follows: Among them, f c >0 is the Coulomb friction coefficient, f v >0 is the viscous friction coefficient, f b is the friction offset value, and sgn(·) is the sign function. For the robot system, D(q), and G(q) are both smooth; Generate a preset trajectory for the workpiece to be ground The impedance model is constructed as follows: in, represents the desired trajectory of the robot after impedance modeling correction, L,B,K∈R 6×6 is a positive definite diagonal matrix, F int represents the interaction force between the mold and the environment measured by the force sensor, and F d represents the expected interaction force.

3. The integral terminal sliding mode trajectory tracking control method based on radial basis function neural network according to claim 2 is characterized in that: The specific process of step 2 is as follows: Assuming that the desired interaction force only exists in the Z-axis direction, and there is no desired interaction force in the X-axis and Y-axis directions, then x d (t) = x p (t), y d (t) = y p (t), the impedance model is rewritten as: Assume that the environment is equivalent to a linear spring, that is f int =k e (With e -With d ),With d <of e ; (8) Among them, z e is the environmental position, k e is the elastic coefficient, the interaction force tracking error f e for: f e =f int -f d =k e (z e -z d )-f d ; (9) but In z p 、z e 、f d Under the condition that all are constants, are all zero, substituting (10) into (7) we get but If and only if When f e =0.

4. The integral terminal sliding mode trajectory tracking control method based on radial basis function neural network according to claim 2 or 3, characterized in that: The specific process of step 3 is as follows: Assumptions Define tracking error η1 = qq d , Get the error dynamic system For a robot dynamic system without interference, that is, τ f ≡0, assuming that the trajectory tracking controller is chosen as: Among them, 0<α1<1, α2=2α1 / (1+α1), v1>0, v2>0, and the expected path can be accurately tracked within a limited time.

5. The integral terminal sliding mode trajectory tracking control method based on radial basis function neural network according to claim 4 is characterized in that: If α1=α2=1, the finite-time trajectory tracking control algorithm will converge to the following control algorithm: This is considered a PD controller based on dynamic compensation.

6. The integral terminal sliding mode trajectory tracking control method based on radial basis function neural network according to claim 4 or 5, characterized in that: The specific process of step 4 is as follows: The radial basis function is expressed as: Among them, c j is the radial basis function data center of the jth neuron in the hidden layer, b j is the width of the radial basis function in the same neuron, and m is the number of input neurons; Assume that there exists a positive constant F such that ‖τ f (t)‖≤F, define a weight matrix Y that satisfies the condition t f (·)=Y T h d (u)+ε; (32) in, is the input of the neural network, ε is the bounded neural network approximation error, is a positive constant; The output of the neural network is: in, is the estimated value of the weight matrix Y; The perturbation approximation error is expressed as Because h d (u) and the weight matrix E are bounded, then we can infer that e f is also bounded, that is is a positive constant; The design of the integral terminal sliding mode trajectory tracking controller based on radial basis function is as follows: in, When 0<α1<1, α2=2α1 / (1+α1), v1>0, v2>0, Under the condition of , the desired trajectory can be tracked within a limited time span.

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