A method for tracking and controlling the sliding mode trajectory of an integral terminal based on a radial basis function neural network.

Abstract

This invention discloses an integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network (RBF neural network), comprising the following steps: constructing an impedance control model based on a dynamic model of a six-DOF industrial robot; designing robot grinding force control logic based on the impedance control model; designing a finite-time trajectory tracking controller based on the robot's dynamic model; designing an integral terminal sliding mode trajectory tracking controller based on an interference approximation method using a radial basis function neural network; and verifying the performance of the integral terminal sliding mode trajectory tracking controller through numerical simulation using a six-DOF robot. This invention addresses the interactive force control problem of industrial robot grinding systems by designing a novel impedance-based finite-time force control algorithm to improve the dynamic performance of industrial robot grinding systems. Compared with existing algorithms, the proposed RBF+ITSMC algorithm exhibits better performance in interactive force tracking speed and accuracy, and possesses superior anti-interference capabilities.

Description

Technical Field

[0001] This invention belongs to the field of robotic arm control technology, specifically a method for tracking and controlling the sliding mode trajectory of an integral terminal based on a radial basis function neural network. Background Technology

[0002] In recent years, many scholars have studied force / position control algorithms and published numerous results. In practical applications, linear methods such as PID control are favored due to their simplicity. However, linear control methods suffer from poor robustness in complex situations due to their reliance on a linearized system model. In the early stages of research, impedance control algorithms were proposed to achieve flexible control of robot manipulators. However, the strong coupling, uncertainties, and external environmental disturbances of robots make ensuring the robustness of these control methods challenging in practical applications. Furthermore, to improve the performance of control algorithms, researchers have introduced various nonlinear control strategies. To address the dynamic force tracking problem, an adaptive control method based on real-time modification of impedance model parameters has been proposed. In some techniques, fuzzy control methods have been used to achieve flexible control of robot arms, demonstrating excellent performance in handling system uncertainties and external disturbances.

[0003] However, the aforementioned algorithm is an asymptotically stable control algorithm, facing the problem of failing to converge to the equilibrium point within a finite time. In contrast, finite-time control systems not only reach convergence 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. It is well known that sliding mode control does not require an accurate system model and improves the system's response speed, thus facilitating the control of complex systems. In sliding mode control, the system rapidly converges from the initial state to a sliding surface and then slides to reach the equilibrium point. However, mismatched disturbances exist in various engineering applications, posing a significant challenge in the design phase of sliding mode controllers.

[0004] To improve the robustness of sliding mode control in uncertain environments, some researchers have introduced integral terms when designing the sliding surface to eliminate the sliding mode arrival phase. Integral Sliding Mode Control (ISMC) has been proven to exhibit superior anti-interference performance. Furthermore, terminal sliding mode control strategies are often used to improve the system's convergence speed. It is worth noting that while terminal sliding mode control can converge in a finite time, it may lead to singularity problems. In view of these points, this invention proposes a scheme combining the above two control theories, thus developing the Integral Terminal Sliding Mode Control (ITSMC) algorithm. This strategy not only achieves system convergence in a finite time but also successfully avoids singularity problems while demonstrating excellent anti-interference performance. Summary of the Invention

[0005] This invention addresses the interactive force control problem in industrial robot grinding systems by designing and applying a novel impedance-based finite-time force control algorithm to improve the dynamic performance of these systems. First, an interactive force control scheme for the grinding system is designed based on an impedance model. Second, a finite-time control algorithm is designed according to the robot's dynamic characteristics. Rigorous theoretical analysis ensures the finite-time stability of the closed-loop system under undisturbed conditions. Third, to improve the system's ability to suppress disturbances, a disturbance approximation method based on radial basis functions (RBF) is employed. Based on this result, a finite-time controller improved through integral terminal sliding mode is designed. Finally, numerical simulation results verify the correctness of the theory.

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A sliding mode trajectory tracking control method for integral terminals based on radial basis function neural networks includes 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 robot grinding force control logic based on impedance control model;

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

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

[0012] Step 5: Perform numerical simulation using a six-DOF robot to verify the performance of the sliding mode trajectory tracking controller of the integrator terminal.

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

[0014] 1. This invention designs an interactive force control scheme for a grinding system based on an impedance model. A finite-time control algorithm is designed according to the robot's dynamic characteristics. Rigorous theoretical analysis ensures the finite-time stability of the closed-loop system under undisturbed conditions. To improve the system's ability to suppress disturbances, a disturbance approximation method based on radial basis functions (RBF) is adopted. Based on this result, a finite-time controller improved by sliding mode integration at the end point is designed, and the correctness of the theory is verified by numerical simulation results.

[0015] 2. This invention addresses the interactive force control problem in industrial robot grinding systems by designing and applying a novel impedance-based finite-time force control algorithm to improve the dynamic performance of industrial robot grinding systems. Compared with existing FTC and PD algorithms, the proposed RBF+ITSMC algorithm demonstrates superior performance in interactive force tracking speed and accuracy, while also exhibiting better anti-interference capabilities. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of a force feedback-based robotic grinding system.

[0017] Figure 2 This is a block diagram illustrating impedance-based robot force control.

[0018] Figure 3 This is a schematic diagram of the perturbation approximation process based on radial basis functions;

[0019] Figure 4 The constant interactive force tracking curve under interference-free conditions;

[0020] Figure 5 The time-varying interactive force tracking curve under interference-free conditions;

[0021] Figure 6 The error curve of time-varying interactive force tracking under interference-free conditions;

[0022] Figure 7 The position tracking curves in the X and Y axes under interference-free conditions;

[0023] Figure 8 The constant interaction force tracking curve under disturbance conditions;

[0024] Figure 9 The perturbation estimation performance is based on radial basis functions, where parts (a) to (f) correspond to the 1st to 6th joints of a six-DOF robot, respectively.

[0025] Figure 10 The figure shows the robot joint tracking error curves under interference conditions, where parts (a) to (f) correspond to the 1st to 6th joints of a six-degree-of-freedom robot, respectively.

[0026] Figure 11 The time-varying interactive force tracking curve under interference conditions;

[0027] Figure 12 The time-varying interactive force tracking error curve under interference conditions;

[0028] Figure 13 The position tracking curves in the X and Y axes are shown under the condition of interference. Detailed Implementation

[0029] The preferred embodiments of the present invention will now be described in detail with reference to 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 providing a clearer and more explicit definition of the scope of protection of the present invention.

[0030] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the specification of this invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The term "or / and" as used herein includes any and all combinations of one or more of the associated listed items.

[0031] A schematic diagram of a force feedback-based robotic grinding system is shown below. Figure 1 As shown, it mainly includes 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] This invention provides an integral terminal sliding mode trajectory tracking control method based on radial basis function neural networks, comprising 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 robot grinding force control logic based on impedance control model;

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

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

[0037] Step 5: Perform numerical simulation using a six-DOF robot to verify the performance of the sliding mode trajectory tracking controller of the integrator terminal.

[0038] The specific process is as follows:

[0039] The general dynamic equations of a six-degree-of-freedom industrial robot are as follows:

[0040]

[0041] in Let τ represent the robot's angle, angular velocity, and angular acceleration, respectively, where τ∈R 6×1 It is the joint torque vector, τ f ∈R 6×1It is the disturbance torque vector, D(q)∈R 6×6 It is the inertia matrix, G(q)∈R 6×1 It is the gravity vector. It is the vector of centripetal force and Coriolis force. This is the friction vector of the robot joints. The frictional force of a robot can usually be described as follows:

[0042]

[0043] Among them, f c >0 is the Coulomb friction coefficient, f v >0 is the coefficient of viscous friction, f b It is the friction offset value, while sgn(·) is the sign function. For the robot system, D(q), Both G(q) and G(q) are smooth. From existing literature, it is known that matrix D(q) is positive definite and symmetric, while matrix... It is obliquely symmetrical. These properties are helpful in controller design.

[0044] definition For a vector For the sake of description, it is represented as

[0045] (Homogeneous space) for e j Given that ∈ >0, j = 1, ..., k, define a vector (e1, ..., e2). k )∈R k For a vector space

[0046]

[0047] if for Ψ>-min{e j If the vector (e1, ..., ek) satisfies the condition, then we can say that for the vector (e1, ..., ek)... k ), vector functions It has homogeneity Ψ∈R. At the same time, the above vector space (3) is called a homogeneous space.

[0048] Consider a perturbed vector space:

[0049]

[0050] Among them, It is a nominal vector space, while the perturbed vector space is... Meet the conditions If the nominal vector space is such that for (e1,…,e...) k It has a homogeneous degree Ψ < 0 and an asymptotically stable equilibrium point. Therefore, the equilibrium point also exhibits finite-time stability. Furthermore, if the perturbation vector space satisfies the condition...

[0051]

[0052] The origin represents a locally stable equilibrium point within the system that has finite-time stability.

[0053] The main objective is to develop a high-precision force and position control algorithm that enables the robotic grinding system to simultaneously track a predefined work trajectory and follow predetermined interaction forces.

[0054] Force control strategy through impedance control:

[0055] For the workpiece to be ground, a preset trajectory is generated according to the grinding requirements. Then, an impedance-based force control algorithm was used to design a high-precision force / position control algorithm, the control block diagram of which is shown below. Figure 2 As shown.

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

[0057]

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

[0059] In the robot's base coordinate system, it is assumed that the desired interaction force exists only in the Z-axis direction, and there is no desired interaction force in the X and Y-axis directions. Therefore, in Figure 2 After the control process shown, the predetermined trajectories in the X and Y axes remain unchanged, i.e., 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 based on the measured interaction forces. Therefore, a high-performance composite perturbation suppression controller needs to be designed to enable the robot to track the desired position.

[0060] The control performance of the impedance-type interactive force control method is analyzed, taking the z-direction as an example.

[0061] Assuming the desired interaction force exists only in the Z-axis direction, and there is no desired interaction force in the X and Y-axis directions, then x d (t)=xp (t), y d (t)=y p (t), the data corresponding to each item in the Z-axis direction in the impedance model (6) above are extracted separately and rewritten as:

[0062]

[0063] Assuming 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] Among them, z e It refers to the environmental position, i.e., the position of the workpiece, z. d It is the expected position in the Z-axis direction, k e It is the elastic coefficient, defined as f. e For interactive force tracking error, f e for:

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

[0067] but

[0068]

[0069] Considering the simplest case of planar interaction force polishing, z p z e f d All are constants; under these conditions, Both are zero. Substituting (10) into (7) yields...

[0070]

[0071] but

[0072]

[0073] According to equation (12), if and only if At that time, f e The condition is true only if the value is 0. When this condition is not met, impedance-based methods for interactive force control will not be able to achieve zero interactive force tracking error.

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

[0075] For the robotic grinding process, under the condition that the robot's operating speed is required to remain at a relatively slow level, we can assume that the desired speed is constant, i.e. Define the tracking error η1 = qq d , q d and Let the desired angle and desired angular velocity of the robot be represented respectively, and the error dynamic system is obtained as follows:

[0076]

[0077] For ease of explanation, D, C, and G will be used as D(q) from now on. It is an abbreviation for G(q). The main goal next is to design an interference suppression control algorithm to achieve η1→0 and η2→0 within a finite time.

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

[0079] For a robot dynamics system without disturbance (1), i.e. τ f ≡0, assuming the trajectory tracking controller is selected as:

[0080]

[0081] Where 0 < α1 < 1, α2 = 2α1 / (1 + α1), v1 > 0, v2 > 0, the desired path can be accurately tracked within a finite time.

[0082] The proof is as follows:

[0083] Substituting equation (14) into equation (13), we can obtain the following dynamic system of robot position error:

[0084]

[0085] Step 1: Prove global asymptotic stability;

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

[0087]

[0088] And by differentiating W1 along the closed-loop system (15), we get

[0089]

[0090] as well as

[0091]

[0092] thereby

[0093]

[0094] Using LaSalles' invariance principle, we can conclude that the origin (η1,η2)=(0,0) of the system is globally asymptotically stable, which means that as t→∞, (η1,η2)→(0,0).

[0095] The second step is to prove the 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 regarding locally stable equilibrium points for finite-time stability will be applied. The closed-loop system (15) can be restated as:

[0097]

[0098] in,

[0099]

[0100] First, we present the nominal system in equation (20), namely

[0101]

[0102] It is globally asymptotically stable and has negative homogeneity. The Lyapunov function is chosen as follows:

[0103]

[0104] Similar to equation (17), through equation (22), I obtain the derivative of W2, that is...

[0105]

[0106] Through the previous processing, according to equation (24), it can be concluded that the nominal system (22) has achieved asymptotic stability. On the contrary, according to the aforementioned definition, the nominal system (22) exhibits a homogeneity of Ψ = (α1-1) / 2 < 0 with respect to the expansion (e1,e1,e1,e1,e1,e1,e2,e2,e2,e2,e2,e2).

[0107] Secondly, for any (η1,η2)≠0, equation (22) satisfies the condition.

[0108] Express a continuously differentiable function as

[0109] g(η1)=D-1 (η1+q d (25)

[0110] Using the AM-GM inequality, we can obtain

[0111]

[0112] Here, O(·) represents the corresponding infinitesimal. Therefore, for any (η1,η2)≠0,

[0113]

[0114] Since Ψ=(α1-1) / 2, e1=1 and e2=(1+α1) / 2, we get:

[0115] e1α1-e2-Ψ=0; (28)

[0116] Substituting this equation into equation (27), we get:

[0117]

[0118] Based on the aforementioned lemma, it can be deduced that the closed-loop system (15) exhibits local finite-time stability. Therefore, combining the findings of the previous two steps, it can be concluded that the closed-loop system (15) achieves global finite-time stability, which means that (η1,η2) tends to zero in a finite time.

[0119] Meanwhile, if α1 = α2 = 1, the finite-time trajectory tracking control algorithm will converge to the following control algorithm:

[0120]

[0121] This is considered a PD controller based on dynamic compensation. 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 with Interference: This embodiment addresses the challenge of tracking industrial robot trajectories by considering interference factors such as unmodeled errors and external disturbances. An improved finite-time trajectory tracking controller is developed by integrating integral sliding mode control and neural networks, capable of completely eliminating interference.

[0123] To handle external interference τ f (t) was estimated using a radial basis function (RBF) neural network, where the radial basis function is expressed as:

[0124]

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

[0126] Suppose there exists a positive constant F such that ||τ|| f Let (t)‖≤F, and define a weight matrix Y that satisfies this condition.

[0127] τ f (·)=Y T h d (u)+ε; (32)

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

[0129] The output of the neural network is:

[0130]

[0131] in, It is an estimate of the weight matrix Y;

[0132] The perturbation approximation error is expressed as

[0133]

[0134] Due to h d If (u) and the weight matrix E are bounded, then it can be inferred that e f It is also bounded, that is It is a normal number.

[0135] The following describes an improved finite-time trajectory tracking controller developed using the Integral Terminal Sliding Mode Control (ITSMC) algorithm based on RBF neural networks, namely the Radial Basis Function-Based Integral Terminal Sliding Mode Control (RBF+ITSMC) trajectory tracking controller.

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

[0137]

[0138] in,

[0139]

[0140] When 0<α1<1, α2=2α1 / (1+α1), v1>0, v2>0, Under these conditions, 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) yields

[0143]

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

[0145] Phase 1: The arrival phase of s.

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

[0147]

[0148] And the derivative of W2 is derived as:

[0149]

[0150] Using the symmetry properties of matrix D and equation (38), we have

[0151]

[0152] in, f (·) denotes the minimum value function, i.e. f (x(t))=min(x(t)).

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

[0154]

[0155] but

[0156]

[0157] Based on existing literature and the above lemma, it can be concluded that the sliding 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 phase, after reaching the next phase, there are

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

[0161]

[0162] Based on the aforementioned assumptions and theorems, it can be deduced that in a finite amount of 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 correctness of the theory. To achieve robotic grinding, the following three control algorithms are used: ① Proportional-Derivative (PD) controller, ② Finite-Time Controller (FTC), and ③ Radial Basis Function-Based Integral Terminal Sliding Mode Controller (RBF+ITSMC). Based on a trial-and-error approach, the gain selections for these three control algorithms are 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, 0.18m) with a radius of R = 0.01m. Simultaneously, the desired interaction force needs to be tracked in the Z direction. Next, the simulation verification mainly focuses on two cases: constant interaction force and time-varying interaction force, as well as the case with and without external disturbances.

[0167] Scenario 1: Under conditions of no interference;

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

[0169] 1) Constant interaction force. The desired contact force is set as... like Figure 4 The figure shows the force tracking curves of three algorithms. The convergence criterion for interaction force tracking is defined as |f(t) - f d (t)|<0.1N. Table 2 shows the number of convergences for interaction force tracking. Based on the above results, it is concluded that RBF+ITSMC and FTC provide faster tracking rates for interaction forces compared to the PD algorithm.

[0170] Table 2 Comparison of convergence times (s) for constant interaction force tracking under undisturbed conditions

[0171]

[0172] 2) Time-varying interaction force. The desired interaction force is set as f. d (t)=(10+10sin(t))N. The force tracking control response curve is as follows: Figure 5 As shown, the interactive force tracking error is as follows: Figure 6 As shown, it is clear that the RBF+ITSMC and FTC algorithms exhibit smaller steady-state errors compared to the PD algorithm. Furthermore, as... Figure 7 The position tracking results along the X and Y axes shown also confirm the above conclusions.

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

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

[0175] 1) Constant interaction force. The desired constant interaction force f d The settings are the same as described above, and the interaction force tracking curve is as follows: Figure 8 As shown. To mitigate the impact of disturbances on the dynamic system, a radial basis function (RBF)-based method is employed to provide approximate estimates of the disturbances, thereby eliminating them. Figure 9 The results of the interference estimation are presented, showing that the RBF-based method can provide effective interference estimation. Furthermore, Figure 10 The robot joint tracking error is presented. It can be seen that, under the presence of interference, the RBF+ITSMC algorithm proposed in this invention exhibits superior interference suppression capability compared to the FTC and PD algorithms.

[0176] 2) Time-varying interaction force. Similarly, choose the same time-varying expected interaction force f as described above. d (t), the interaction force tracking curve and tracking error are respectively in Figure 11 and Figure 12 This is shown in the image. Furthermore, X-axis and Y-axis position tracking is also shown in... Figure 13 The results are given in Table 3. Table 3 presents the steady-state errors of constant and time-varying interaction forces when the system is affected by external disturbances. All the above results demonstrate the excellent disturbance suppression capability of the RBF+ITSMC algorithm.

[0177] Table 3 Comparison of steady-state errors (N) in interactive force tracking under disturbance conditions.

[0178]

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

[0180] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.

[0181] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for integral terminal sliding mode trajectory tracking control based on a radial basis function neural network, characterized in that, Comprising the following steps: Step 1, constructing impedance control model based on dynamic model of 6-DOF industrial robot; The specific process of this step is as follows: The dynamics equation of 6-DOF industrial robot is: ； （1） where , , , respectively represent the angle, velocity and acceleration of the robot, is the joint torque vector, is the disturbance torque vector, is the inertia matrix, is the gravity vector, is the centripetal and Coriolis force vector, is the robot joint friction vector, the friction force of the robot is described as follows: ； （2） wherein is the Coulomb friction coefficient, is the viscous friction coefficient, is the friction offset value, and is the sign function, for the robot system, , and are all smooth; For a workpiece to be ground, a preset trajectory is generated ; The impedance model is constructed as follows: ； （6） wherein, represents the robot desired trajectory corrected by impedance modeling, is a positive definite diagonal matrix, represents the interaction force between the grinding tool and the environment measured by the force sensor, while represents the desired interaction force; Step 2, designing robot grinding force control logic based on impedance control model; Step 3, designing finite time trajectory tracking controller based on dynamic model of robot; The specific process of this step is as follows: Assume , define the tracking error , , and denote the desired angle and desired angular velocity of the robot, respectively, resulting in the error dynamics ； （13） wherein , , and are the short names for the matrices , , and , respectively; For a robot dynamics system without disturbance, i.e. , assume that the trajectory tracking controller is chosen as: ； （14） wherein, , , , , can accurately track the desired path in a limited time; Step 4, designing integral terminal sliding mode trajectory tracking controller based on disturbance approximation method of radial basis function neural network; Step 5, verifying the performance of integral terminal sliding mode trajectory tracking controller through numerical simulation of 6-DOF robot.

2. The integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network according to claim 1, 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 , , the impedance model is rewritten as: ； （7） wherein , , , , , , , , , respectively , , , , , , , , , , values of the respective data extracted individually with respect to the Z-axis direction; Assume that the environment is equivalent to a linear spring, that is ， ； （8） wherein, is the environmental position, is the elastic coefficient, the interaction force tracking error is: ； （9） Then ； （10） In , , are constants, under the condition that , , , are zero, (10) is substituted into (7) to obtain ； （11） Then ； （12） if and only if , .

3. The integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network according to claim 1 or 2, characterized in that: If , the finite-time trajectory tracking control algorithm will converge to the following control algorithm: ； （30） This is regarded as a PD controller based on dynamic compensation.

4. The integral terminal sliding mode trajectory tracking control method based on a radial basis function neural network according to claim 3, characterized in that, The specific process of step 4 is as follows: The radial basis function is expressed as: ， ； （31） wherein, is the radial basis function data center for the th neuron of the hidden layer, is the radial basis function width in the same neuron, is the number of terms for the input neuron; Let us assume that there exists a positive constant such that , is an external disturbance, define a weight matrix that satisfies the condition ； （32） wherein, is an input to the neural network, is a bounded neural network approximation error, , is a positive constant; The output of the neural network is: ； （33） wherein, is an estimate of the weight matrix Y; The disturbance approximation error is expressed as ； （34） Since and the weight matrix Y is bounded, it follows that is also bounded, i.e. , is a positive constant; The design of integral terminal sliding mode trajectory tracking controller based on radial basis function is as follows: ；（35） Wherein, ； （36） is the short form of is the short form of is the short form of , , , , under the condition that the desired trajectory can be tracked within a finite time span.

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