Mechanical arm rbf network dynamic adaptive control method under time-varying mechanism constraint

Abstract

The application belongs to the field of robot technology control, and particularly relates to a mechanical arm RBF network dynamic self-adaptive control method under time-varying mechanism constraint, which comprises the following steps: constructing a mechanical arm dynamics model, determining a system prescribed time convergence standard, defining a trajectory tracking error in combination with a joint motion reference trajectory of the mechanical arm, constructing a stable robust control law of the nominal dynamics model under the prescribed time based on the nominal dynamics model, selecting a radial basis function, and designing an RBF network self-adaptive control law under the prescribed time to dynamically fit comprehensive nonlinear disturbance items in the system. The application solves the uncontrollable problem of convergence time of the traditional method, dynamically approximates the comprehensive disturbance by using the RBF neural network, updates the network weight online through the adaptive law of the time-varying gain, significantly improves the anti-interference ability, combines the model driving method with the data driving method, realizes more accurate and low-time-delay trajectory tracking control through the decoupling and feedforward compensation strategy of the dynamics model.

Description

Technical Field

[0001] This invention belongs to the field of robot technology control, specifically relating to a dynamic adaptive control method for a robotic arm using an RBF network under time-varying mechanism constraints. Background Technology

[0002] Robust control of intelligent agents is one of the core research directions in the field of intelligent manufacturing. Robotic arms, as the core execution unit, are widely used in high-precision operations such as precision assembly, logistics handling, and welding. Currently, commonly used control methods mainly include: PD feedback control based on accurate dynamic models. While this method can achieve accurate tracking performance of the robotic arm, its control performance significantly degrades when faced with unmodeled dynamic disturbances; and sliding mode control, which uses a sliding surface to converge the system state asymptotically. Although it exhibits good robustness to external disturbances and parameter uncertainties, it has the inherent drawback of not being able to precisely guarantee the convergence time. These traditional control methods lead to the following key challenges for robotic arms in actual operation: unmodeled dynamics and parameter uncertainties, external disturbance suppression, and convergence speed and time constraints.

[0003] Compared with existing technologies, although RBF neural networks can approximate unknown nonlinearities, traditional weight update laws have slow convergence speed and lack time constraint mechanisms; existing time-varying gain methods (such as terminal sliding mode) can achieve finite-time convergence, but require known upper bounds of perturbations and have singularity problems; methods combining nominal models and perturbation observers (such as ADRC) require complex parameter tuning, which limits their engineering practicality. Summary of the Invention

[0004] To effectively address the problem of precise control of robotic arms in complex dynamic environments and provide a reliable solution for scenarios requiring millimeter-level response and synchronous control, such as intelligent manufacturing and industrial automation, this invention proposes a dynamic adaptive control method for robotic arms using a Radial Basis Function (RBF) network under time-varying constraints. This method includes constructing a dynamic model of the robotic arm, determining the system's convergence criterion over a specified time, defining the trajectory tracking error based on the reference trajectory of the robotic arm's joint motion, constructing a stable and robust control law for the nominal dynamic model under a specified time based on the nominal dynamic model, selecting radial basis functions, and designing an adaptive control law for the RBF network under a specified time to dynamically fit the comprehensive nonlinear disturbance terms in the system.

[0005] Furthermore, the dynamic adaptive control law of the RBF network under a given time is expressed as:

[0006]

[0007] Where, τ 总M0(q) represents the dynamic adaptive control law of the RBF network under a specified time; M0(q) is the nominal inertia matrix of the robotic arm system, and q represents the actual joint rotation position vector of the robotic arm system. k represents the desired acceleration reference trajectory of the robotic arm system. v This represents the control gain matrix of the second design; This represents the joint velocity tracking error scaled based on the time-varying gain function; k p Represents the first design control gain matrix; η represents the joint angle tracking error signal scaled based on the time-varying gain function; The nominal Coriolis force matrix of the robotic arm system; G0(q) represents the actual joint velocity vector of the robotic arm system; G0(q) is the nominal gravity vector of the robotic arm system. This is the real-time estimated output value of the RBF for the integrated disturbance nonlinear term.

[0008] Furthermore, the RBF provides a real-time estimate of the nonlinear term of the integrated disturbance. Represented as:

[0009]

[0010] in, This is an online estimate of the weights of the RBF neural network; h(x) = [h1(x),...,h... m (x)] T The output vector of the radial basis functions. Let q represent the input state vector of the RBF neural network, and let q represent the current joint rotation position vector of the robotic arm system. This represents the current joint motion velocity vector of the robotic arm system. This represents the current joint motion acceleration vector of the robotic arm system, and m represents the number of nodes in the hidden layer of the RBF neural network.

[0011] Furthermore, when calculating the dynamic adaptive control law of the RBF network under a specified time, the approximation error of the RBF neural network for the comprehensive nonlinear disturbance term is less than or equal to the upper bound of the approximation error of the RBF neural network for the comprehensive nonlinear disturbance term. The approximation error of the RBF neural network for the comprehensive nonlinear disturbance term is:

[0012]

[0013] Where σ(x) is the approximation error of the RBF neural network for the integrated nonlinear perturbation term; To synthesize the nonlinear disturbance term, it is expressed as: ΔM represents the uncertainty of the inertial parameters of the robotic arm system, ΔC represents the modeling error of the Coriolis force matrix of the robotic arm system, ΔG represents the gravity compensation residual of the robotic arm system, and d is the unknown external environmental disturbance vector; w * This represents the ideal weights of the RBF neural network.

[0014] Furthermore, the online estimation of the weights of the RBF neural network... The adaptive update law is:

[0015]

[0016] Where γ is the adaptive learning rate; μ(t) is the time-varying gain function; h(x) = [h1(x),...,h m (x)] T The output vector of the radial basis function; Let η be the error state vector, representing the joint angle tracking error scaled based on the time-varying gain function. denoted by , representing the joint velocity tracking error scaled by the time-varying gain function; P is the solution matrix of the Lyapunov function; B represents the inertia matrix.

[0017] Furthermore, the calculation of the error state vector includes:

[0018] η(t)=μ(t)e(t)

[0019]

[0020] Where η(t) is the joint angle tracking error scaled by the time-varying gain function at time t, and e(t) is the error between the actual joint angle trajectory at time t and the expected joint angle trajectory at time t; The joint velocity tracking error at time t is scaled based on the time-varying gain function. Let be the difference between the actual joint velocity trajectory at time t and the expected joint velocity trajectory at time t. Let t be the time derivative of the time-varying gain function.

[0021] Furthermore, the solution matrix P of the Lyapunov function satisfies the following condition:

[0022] A T P + PA = -Q

[0023] in, Represented as the design control gain parameter matrix, I n Let represent an n×n identity matrix, where n is the degree of freedom of the robotic arm system, and Q represents a positive definite symmetric matrix.

[0024] Furthermore, the first design control gain matrix is ​​expressed as follows: The second design control gain matrix is ​​expressed as follows: α is a design positive constant.

[0025] Furthermore, when the preset convergence time is T, the Lyapunov function of the system is bounded in the region [0, T), and the time convergence criterion is defined as follows:

[0026]

[0027] in, V(t) represents the time derivative of the Lyapunov function of the system; k and θ are positive constants; V(t) represents the Lyapunov function of the system; d(t) represents the unknown disturbance of the system.

[0028] Furthermore, the dynamic model of the n-degree-of-freedom robotic arm is expressed as:

[0029]

[0030] in, It is a positive definite inertia matrix; The Coriolis force matrix; d is the gravity vector; d is the unknown external environmental disturbance vector; Let be the input torque of the joint, and q represent the current joint rotation position vector of the robotic arm system. This represents the current joint motion velocity vector of the robotic arm system. This represents the current joint motion acceleration vector of the robotic arm system.

[0031] This invention addresses the challenges faced by robotic arms in real-world operating conditions, including unmodeled dynamics and external disturbances. It proposes a time-defined RBF neural network architecture, which achieves the following technological breakthroughs by introducing a time-varying gain mechanism: precise time-converged control, where the designed control algorithm ensures global convergence of the system's nonlinear model approximation error within a user-preset time, solving the problem of uncontrollable convergence time in traditional methods; intelligent disturbance compensation, employing an RBF neural network to dynamically approximate the comprehensive disturbance and updating network weights online through an adaptive law of time-varying gain, significantly improving anti-interference capability; and innovatively combining model-driven and data-driven methods, achieving more precise and low-latency trajectory tracking control through dynamic model decoupling and feedforward compensation strategies. Compared to existing technologies, the proposed time-defined RBF network dynamic adaptive control achieves precise convergence within a user-preset time and significantly enhances anti-interference capability. Attached Figure Description

[0032] Figure 1 This is a flowchart of a dynamic adaptive control method for a robotic arm using an RBF network under time-varying mechanism constraints, as described in this invention.

[0033] Figure 2 This is a Simulink framework diagram of the dynamic adaptive control of the RBF network in this invention;

[0034] Figure 3 This is a schematic diagram showing how the actual rotational trajectories of robotic arm joint 1 and robotic arm joint 2 track the desired rotational trajectory when the specified time is 1 second.

[0035] Figure 4 This is a schematic diagram showing how the actual speed trajectories of robotic arm joint 1 and robotic arm joint 2 track the desired speed trajectory when the specified time is 1 second.

[0036] Figure 5 This is a schematic diagram of the control input of robotic arm joint 1 and robotic arm joint 2 during a specified time of 1 second.

[0037] Figure 6 This is a schematic diagram of the RBF approximation nonlinear disturbance of robotic arm joint 1 and robotic arm joint 2 at a specified time of 1 second.

[0038] Figure 7 This is a schematic diagram showing how the actual rotational trajectories of robotic arm joint 1 and robotic arm joint 2 follow the desired rotational trajectory at a specified time of 0.5s. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] This invention proposes a dynamic adaptive control method for a robotic arm using a Radial Basis Function (RBF) network under time-varying constraints. The method includes constructing a dynamic model of the robotic arm, determining the system's convergence criterion over a specified time, defining the trajectory tracking error based on the joint motion reference trajectory of the robotic arm, constructing a stable and robust control law for the nominal dynamic model under a specified time based on the nominal dynamic model, selecting radial basis functions, and designing an adaptive control law for the RBF network under a specified time to dynamically fit the comprehensive nonlinear disturbance term in the system.

[0041] This embodiment proposes a dynamic adaptive control method for a robotic arm using an RBF network under time-varying mechanism constraints, such as... Figure 1 As shown, the method includes the following:

[0042] S1: Construct a dynamic model of the robotic arm and determine the system's time-limited convergence criterion.

[0043] This embodiment considers a robotic arm with n degrees of freedom, whose dynamic model can be expressed as:

[0044]

[0045] in, It is a positive definite inertia matrix; The Coriolis force matrix (including centrifugal force and Coriolis force); d is the gravity vector; d is the unknown external environmental disturbance vector; Let be the input torque of the joint, i.e., the control input vector, and q represent the current joint rotation angle position vector of the robotic arm system. This represents the current joint motion velocity vector of the robotic arm system. This represents the current joint motion acceleration vector of the robotic arm system.

[0046] When the preset convergence time is T, that is, the actual control and the desired control of the robotic arm reach consistency within the latest convergence time, the Lyapunov function of the system is bounded in the region [0,T). The time convergence criterion is defined as follows:

[0047]

[0048] in, denoted by , where k and θ are positive constants greater than 0, μ(t) represents the time-varying gain function, V(t) represents the system's Lyapunov function, and d(t) represents the unknown disturbance of the system.

[0049] Furthermore, considering the time-varying gain function μ(t), if there exists a smooth function V: [0,T)→[0,+∞) satisfying the inequality:

[0050] For d(t) to be an unknown disturbance, and k and θ > 0 to be positive constants, then V(t) is bounded in the time interval [0, T).

[0051] Among them, when the system control process time t approaches the preset convergence time T, that is, (t→T) - As the time-varying gain function μ(t) approaches infinity, to prevent unbounded gain, the expression for the time-varying gain function μ(t) is further expressed as:

[0052]

[0053] Where t represents the time during the control process of the robotic arm system, T represents the user-specified convergence time, δ represents the coefficient of the safe transition interval, and μ max μ represents the upper bound for preventing the time-varying gain function from growing unbounded. minβ represents the lower limit of the steady-state time-varying gain, p represents the order of the robotic arm system, and β represents the positive design parameter.

[0054] The dynamic model of the robotic arm system includes a nominal part and an unmodeled (unknown) part, specifically described as follows:

[0055] ΔM=M0-M

[0056] ΔC=C0-C

[0057] ΔG=G0-G

[0058] in, Let M(q) represent the nominal inertia matrix, nominal Coriolis force matrix (including Coriolis force and centrifugal force), and nominal gravity vector of the robotic arm system, respectively. Let ΔM, ΔC, and ΔG represent the uncertainty of the inertial parameters, the uncertainty of the Coriolis force matrix, and the gravity compensation residual of the robotic arm system, respectively. M(q) is the positive definite inertia matrix of the robotic arm system. G(q) is the Coriolis force matrix of the robotic arm system; G(q) is the gravity vector of the robotic arm system.

[0059] Based on a clear understanding of the dynamic characteristics, the following assumptions are introduced:

[0060] Assumption 1: For any time The system satisfies that the reference trajectory and its derivative are continuous and bounded, that is:

[0061]

[0062] Where, q d (t), These represent the desired joint rotation angle, velocity, and acceleration trajectory, respectively. Let be a known positive constant, and ||·|| denote the L2 norm.

[0063] The unknown disturbance d(t) is bounded, that is:

[0064]

[0065] in, Represents an unknown but bounded positive integer.

[0066] S2: Define the trajectory tracking error.

[0067] Based on the joint motion reference trajectory of the robotic arm, the joint rotation angle tracking error e(t) and the joint velocity tracking error are defined. They are respectively:

[0068]

[0069] in, This is represented as the actual joint rotation position vector at time t. Let t be the expected joint angle trajectory. This is represented as the actual joint velocity vector at time t. This is represented as the expected joint velocity trajectory at time t.

[0070] Based on the time-controlled theory, the tracking error is dynamically scaled according to the time-varying gain function μ(t). Therefore, the scaled joint angle tracking error signal η(t) and the speed tracking error signal are similar. They can be represented as:

[0071] η(t)=μ(t)e(t)

[0072]

[0073] Where μ(t) represents the time-varying scaling function, which can be expressed as: The time derivative of the time-varying gain function It can be represented as:

[0074]

[0075] Where p represents the order of the robotic arm system, and β represents the positive design parameter.

[0076] S3: Based on the nominal dynamic model, construct a stable and robust control law for the nominal dynamic model at a specified time.

[0077] Substituting the nominal model described in step 1 into the original dynamic model, it can be expressed as:

[0078]

[0079] in, This represents the comprehensive nonlinear perturbation term, including the unmodeled dynamics and the external perturbation d.

[0080] Based on the nominal dynamics model, the prescribed time control law under the condition that the comprehensive nonlinear disturbance term is known is:

[0081]

[0082] in, This represents the joint control input vector based on the nominal dynamics model. These are respectively represented as the nominal inertia matrix, nominal Coriolis force matrix (including Coriolis force and centrifugal force), and nominal gravity vector of the robotic arm system. This represents the desired acceleration reference trajectory. k represents the actual joint velocity vector. p The first design control gain matrix can be represented as: α > 0 indicates a positive constant, k v The second design control gain matrix can be represented as follows: To synthesize the nonlinear disturbance term, it can be expressed as: ΔM, ΔC, and ΔG represent the inertial parameter uncertainty, Coriolis force matrix modeling error, and gravity compensation residual of the robotic arm system, respectively; d represents an unknown but bounded disturbance; and η and These represent the joint angle tracking error signal and the joint velocity tracking error, respectively, scaled based on the time-varying gain function.

[0083] S4: Select radial basis functions and design an adaptive control law for the RBF network under a specified time to dynamically fit the comprehensive nonlinear disturbance in the system.

[0084] Due to the comprehensive nonlinear disturbance term In practical engineering, the unknown is often present. Approximation and compensation using a radial basis function (RBF) neural network estimator can be expressed as:

[0085]

[0086] in, Represents the input state vector. This represents the real-time estimated output vector of the RBF for the integrated perturbation nonlinear term. This provides an online estimate of the weights for the RBF neural network. Let be the output vector of the Gaussian radial basis functions. Each Gaussian function can be represented as:

[0087]

[0088] In the formula, With b i >0 represents the center vector and width parameter of the i-th radial basis function, respectively, and m represents the number of nodes in the hidden layer.

[0089] A general approximation theory based on RBF neural networks is proposed for any given approximation accuracy ε > 0 and unknown comprehensive nonlinear perturbation terms. There exists an ideal weight matrix Make:

[0090]

[0091] in, For a compact set in the system's state space, the ideal weights w * Determined by the criterion of minimizing the maximum approximation error

[0092] Define the approximation error of the RBF neural network for the synthesized nonlinear perturbation term as:

[0093]

[0094] in, To approximate the error vector of the integrated perturbation nonlinear term, w *T h(x) represents the optimal neural network output, and there exists a positive constant σ0 such that:

[0095]

[0096] Where the upper bound σ0 is defined as

[0097] In summary, the adaptive control law of the RBF dynamic network under a given time can be expressed as:

[0098]

[0099] in, The real-time estimated output value of the RBF for the integrated disturbance nonlinear term can be expressed as: These are online estimates of the weights of the RBF neural network.

[0100] Substituting the adaptive control law into the original dynamic model of the robotic arm, the following closed-loop system characteristics are obtained:

[0101]

[0102] The left side of the equation represents the ideal second-order error dynamics, while the right side represents the residual approximation by the neural network.

[0103] The above equation can be transformed into the error state space matrix form as follows (i.e., the scaled joint rotation angle and velocity error update rate):

[0104]

[0105] in, Let be the error state vector. Represented as the design control gain parameter matrix, I n Represents an n×n identity matrix; M represents the inertia matrix. o (q) represents the nominal inertia matrix of the robotic arm system. Represented as the weight estimation error matrix, This represents the bounded approximation error of the RBF network.

[0106] Based on Lyapunov stability theory and the time-varying gain function μ(t), the adaptive update law for neural network weights over a specified time is designed as follows:

[0107]

[0108] in, This represents the adaptive update law for the weights of the RBF network, where γ > 0 represents the adaptive learning rate; P = P T >0 indicates that the solution matrix of the Lyapunov function satisfies Q is a positive definite symmetric matrix used to specify the system's convergence performance. This indicates that Q is a positive definite matrix.

[0109] S5: Integrating the above components, it enables high-precision position and speed tracking of the robotic arm within a user-specified time.

[0110] Consider a fully driven system of an n-DOF robotic arm, with unmodeled and dynamic external disturbances, given the joint rotation angle q of the robotic arm. d With speed The reference trajectory can be used to achieve stable tracking control within a user-defined time T using the following controller, whose control law can be expressed as:

[0111]

[0112] Based on the above control law, the tracking control of the robotic arm joint angle and joint speed within the user-specified time can be finally achieved.

[0113] like Figure 2 As shown, a dynamic adaptive control method for a robotic arm using an RBF network under time-varying mechanism constraints includes a reference trajectory generator (Input module), a controller (ctrl module) including error transformation, time-defined RBF neural network perturbation approximation, and neural network weight adaptive estimation modules, and an actuator (Plant module).

[0114] The reference trajectory generator Input module mainly generates the desired rotation angle and desired velocity trajectory of the control system. The controller Ctrl module mainly generates the control input torque of the entire system by transforming the desired rotation angle and desired velocity trajectory through error transformation, approximation by RBF neural network perturbation within a specified time, and adaptive estimation of neural network weights. The actuator Plant module mainly inputs the control torque into the entire robotic arm system to achieve stable tracking of the desired trajectory by the robotic arm within a specified time.

[0115] To verify the effectiveness of the method of the present invention, simulation experiments were conducted using MATLAB 2018b and its Simulink module, as detailed below:

[0116] Numerical simulation experiments were conducted to construct a two-degree-of-freedom articulated robotic arm system by selecting appropriate model parameters, in order to verify the effectiveness of the proposed dynamic adaptive control method for the robotic arm under time-varying mechanism constraints using an RBF network. The dynamic parameters are shown in Table 1, and the control parameters are shown in Table 2.

[0117] Table 1. Dynamic parameters

[0118]

[0119] Among them, M 11 Let M denote the first symmetric positive definite inertia matrix of the two-degree-of-freedom robotic arm. 12 M represents the second symmetric positive definite inertia matrix of a two-degree-of-freedom robotic arm. 21 M represents the third positive definite inertial symmetric matrix of a two-degree-of-freedom robotic arm. 22 This indicates that the two-degree-of-freedom robotic arm has fourth positive definite inertial symmetry; C 11 C represents the first Coriolis force of a two-degree-of-freedom robotic arm. 12 C represents the first centrifugal force of a two-degree-of-freedom robotic arm. 21 C represents the second Coriolis force of a two-degree-of-freedom robotic arm. 22 q represents the second centrifugal force of the two-degree-of-freedom robotic arm; v represents the equivalent moment of inertia of the first joint of the robotic arm; q represents the second centrifugal force of the two-degree-of-freedom robotic arm. 01 The moment of inertia of the second joint, q 02 denoted by , where represents the coupling inertia coefficient, and g represents the standard value of gravitational acceleration.

[0120] Table 2 Control Parameters

[0121]

[0122] like Figure 2 As shown, α represents the first control increasing matrix. Second design control gain matrix The positive constant γ represents the adaptive learning rate, k1 represents the design parameters, Q represents the positive definite inertia matrix, and c i Let b be the center vector of the i-th radial basis function in the RBF neural network. i μ represents the width of the i-th radial basis function. max This represents the upper bound of the adjustment of the time-varying gain function, preventing the time-varying gain from growing unbounded. μ min δ represents the steady-state lower limit of the time-varying gain, and δ represents the safety process interval coefficient of the time-varying gain.

[0123] The dynamic model of a two-degree-of-freedom robotic arm can be expressed as:

[0124]

[0125] in:

[0126]

[0127] Let the desired tracking commands for joint angle and angular velocity be:

[0128]

[0129] External disturbances to the system are Where d1 = 2, d2 = 3, d3 = 6, and the initial state of the system is [q1 q2 q3 q4]. T =[0.6 0.3 0.5 0.5] T q1, q2, q3, and q4 represent the initial angles of the first and second joints of the robotic arm, the initial angular velocity of the first joint, and the initial angular velocity of the second joint, respectively. Assuming that the unmodeled dynamic model is ΔM = 0.2M, ΔC = 0.2C, and ΔG = 0.2G, these represent a 20% modeling error in the inertia matrix, a 20% error in the Coriolis force matrix, and a 20% deviation in gravity compensation, respectively.

[0130] Assume the total system simulation time is set to 20 seconds, i.e., t total =20s, sampling period is Δt=0.01s, initial weights of RBF neural network are w=0.1, time-varying gain functions are p=1 and β=2, other design parameters are referred to Tables 1 and 2, and the dynamic adaptive control law of RBF network under specified time proposed in this invention (described by S5) is adopted. Simulation results are as follows. Figures 3 to 7 .

[0131] Figure 3 , Figure 4 The position, rotation angle, and velocity tracking errors of joint 1 and joint 2 of the robotic arm are shown respectively. It is clear from the figures that the time-varying gain mechanism effectively defines the error fluctuation range. Within the user-defined time T = 1 second, the actual trajectory of the robotic arm joint matches the expected trajectory, verifying the system's high precision and rapid response capability. Figure 5 The control input signal of the robotic arm was demonstrated. Under the action of the dynamic adaptive rate of the RBF network, the control input can be kept stable within a certain range without high-frequency chattering, thus verifying the engineering feasibility of the algorithm. Figure 6 This demonstrates the approximation accuracy of the RBF neural network for nonlinear disturbances in the system. Although the initial fluctuations were large, the combination of time-varying gain and RBF achieved a precise approximation within the user-specified time frame, improving its ability to handle dynamic disturbances in real-world operating conditions. Figure 3 and Figure 7 The comparison shows that as the preset time is shortened to 0.5s, the joint rotation angle of the robotic arm can be tracked well within the specified time, which verifies the adaptability of the proposed control method to strict time constraints.

[0132] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A dynamic adaptive control method for a robotic arm using an RBF network under time-varying constraints, comprising constructing a robotic arm dynamics model, determining a system convergence criterion within a specified time, defining a trajectory tracking error based on the joint motion reference trajectory of the robotic arm, and constructing a stable and robust control law for the nominal dynamics model within a specified time based on the nominal dynamics model, characterized in that: Radial basis functions are selected, and an adaptive control law using an RBF network is designed for a specified time to dynamically fit the comprehensive nonlinear disturbance term in the system. For a fully driven system of an n-DOF manipulator, there are unmodeled and dynamic external disturbances. Given the joint rotation angle of the manipulator... With speed Based on the reference trajectory, stable tracking control within a user-defined time T is achieved using the following controller, whose control law is expressed as: in, This represents the dynamic adaptive control law of the RBF network over a specified time. Here is the nominal inertia matrix of the robotic arm system; This represents the desired acceleration reference trajectory of the robotic arm system; This represents the control gain matrix of the second design; This represents the joint velocity tracking error scaled based on the time-varying gain function; This represents the control gain matrix of the first design; This represents the joint angle tracking error signal scaled based on the time-varying gain function; The nominal Coriolis force matrix of the robotic arm system; This is the nominal gravity vector of the robotic arm system. This is the real-time estimated output value of the RBF for the integrated disturbance nonlinear term; The output vector of the radial basis functions. Let represent the input state vector of the RBF network, and q represent the current joint rotation position vector of the robotic arm system. This represents the current joint motion velocity vector of the robotic arm system. This represents the current joint motion acceleration vector of the robotic arm system, and m represents the number of nodes in the hidden layer of the RBF neural network; These are online estimates of the weights of the RBF neural network. Adaptive learning rate; This is the error state vector; Let be the solution matrix of the Lyapunov function; Represents the inertia matrix; time-varying gain function. Represented as: Where t represents the time during the control process of the robotic arm system. The coefficient representing the safe transition range, This represents the upper limit to prevent the time-varying gain function from growing unbounded. This represents the lower bound of the stable time-varying gain. Indicates the order of the robotic arm system. This is represented as a positive design parameter.

2. The method according to claim 1, characterized in that, When calculating the dynamic adaptive control law of the RBF network under a specified time, the approximation error of the RBF neural network for the comprehensive nonlinear disturbance term is less than or equal to the upper bound of the approximation error of the RBF neural network for the comprehensive nonlinear disturbance term. The approximation error of the RBF neural network for the comprehensive nonlinear disturbance term is: in, This represents the approximation error of the RBF neural network for the integrated nonlinear perturbation term. To synthesize the nonlinear disturbance term, it is expressed as: , This indicates the uncertainty of the inertial parameters of the robotic arm system. This indicates the modeling error of the Coriolis force matrix of the robotic arm system. Let d represent the gravity compensation residual of the robotic arm system, and d be the unknown external environmental disturbance vector. This represents the ideal weights of the RBF neural network.

3. The method according to claim 1, characterized in that, The calculation of the error state vector includes: in, The joint angle tracking error at time t is the result of scaling based on the time-varying gain function. The error between the actual joint rotation trajectory at time t and the expected joint rotation trajectory at time t; The joint velocity tracking error at time t is scaled based on the time-varying gain function. Let be the difference between the actual joint velocity trajectory at time t and the expected joint velocity trajectory at time t. This is the time derivative of the time-varying gain function.

4. The method according to claim 1, characterized in that, The solution matrix P of the Lyapunov function satisfies the following condition: in, This is represented as the design control gain parameter matrix. Represent a The identity matrix, This represents a positive definite symmetric matrix.

5. The method according to claim 1 or 4, characterized in that, The first design control gain matrix is ​​represented as follows: ; The second design control gain matrix is ​​expressed as follows: , To design positive constants.

6. The method according to claim 1, characterized in that, When the preset convergence time is T, the system's Lyapunov function in the region The time-bounded condition is defined as follows: in, This represents the time derivative of the Lyapunov function of the system; For positive integers, Represents the Lyapunov function of the system; This indicates an unknown disturbance in the system.

7. The method according to claim 1, characterized in that, The dynamic model of a robotic arm with n degrees of freedom is expressed as: in, It is a positive definite inertia matrix; The Coriolis force matrix; It is the gravity vector; The vector represents the unknown external environmental disturbance. This is the input torque of the joint.

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