Self-adaptive robust control method for hydraulic mechanical arm based on network structure optimization

Abstract

The invention discloses a self-adaptive robust control method for a hydraulic mechanical arm based on network structure optimization. The method comprises the following steps: optimizing a radial basis function neural network offline based on system prior data by using a clustering algorithm to obtain an optimal center vector and a width parameter; designing an adaptive robust controller by using a backstepping method, replacing an actually measured state signal with an expected trajectory signal in a model compensation item, compensating an unmodeled dynamic state on line by using a neural network, and designing a parameter online adaptive law with a correction item to perform weight updating; and the adaptive robust controller outputs control input voltage after processing, and valve port control voltage is obtained through static mapping to control the hydraulic valve. According to the method, the approximation efficiency of the neural network can be effectively improved, the noise of the sensor is inhibited, and high-precision motion tracking of the multi-degree-of-freedom hydraulic mechanical arm is realized.

Description

Technical Field

[0001] This invention relates to a control method for a hydraulic robotic arm, specifically an adaptive robust control method for a hydraulic robotic arm based on network structure optimization. Background Technology

[0002] Multi-degree-of-freedom hydraulic robotic arms are widely used in heavy-duty operations due to their high power density. However, the inherent high-order nonlinearities (such as fluid dynamics and valve characteristics) and parameter uncertainties (such as the friction coefficient varying with temperature) of hydraulic systems pose significant challenges to precise control. Traditional model-based control methods rely on accurate models, while existing adaptive control typically uses measured signals (such as velocity obtained by differentiating position signals) to construct regression matrices for compensation. This amplifies sensor noise and introduces delays, reducing control performance. On the other hand, Radial Basis Function Neural Networks (RBFNNs) are often used to approximate unmodeled dynamics, but the center and width parameters of traditional RBFNNs are usually determined through random initialization or trial and error, resulting in redundant network structures, slow convergence speeds, and high computational loads, making it difficult to meet the real-time control requirements of hydraulic robotic arms. Summary of the Invention

[0003] To address the problems existing in the background technology, this invention provides an adaptive robust control method for hydraulic robotic arms based on network structure optimization. This method solves the problems of low computational efficiency and poor noise resistance in hydraulic robotic arm control.

[0004] The technical solution adopted in this invention is: The adaptive robust control method for hydraulic robotic arms based on network structure optimization of the present invention includes: The first step is to design an adaptive robust controller based on the dynamic model of the multi-degree-of-freedom hydraulic manipulator using the backstepping method. The dynamic model of the multi-degree-of-freedom hydraulic manipulator includes parameter uncertainties, uncertain nonlinearities, and unmodeled dynamics.

[0005] The second step involves acquiring system data of a multi-degree-of-freedom hydraulic manipulator, performing clustering optimization to obtain the center vector and width parameters as inputs to a radial basis function neural network (RBFNN), and designing an online adaptive law for the parameters of the RBFNN.

[0006] The third step involves inputting the system data, along with the center vector and width parameters, into the Radial Basis Function Neural Network (RBFNN). The estimated weight vector of the RBFNN is then updated using an online adaptive law. The RBFNN processes and outputs a neural network fitting term, which is then input into an adaptive robust controller along with the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. After processing, the controller outputs a control input voltage. This control input voltage is then statically mapped to obtain the valve control voltage, which in turn controls the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator.

[0007] In the first step, the adaptive robust controller obtains nonlinear robust feedback terms and basic control terms for torque and flow rate based on the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. These terms, together with the neural network fitting terms output by the radial basis function neural network (RBFNN), are used to obtain the virtual control torque and the desired output flow rate, thereby obtaining the desired output flow rate of the multi-degree-of-freedom hydraulic manipulator.

[0008] The adaptive robust controller is as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] in, The control input voltage for a multi-degree-of-freedom hydraulic robotic arm; It is a statically mapped voltage function; , , , , and These are, respectively, virtual control flow and its expected compensation term, linear feedback term, nonlinear robust feedback term, backstepping compensation term, and neural network fitting term; , , , and These are, respectively, the virtual control torque and its expected compensation term, the linear feedback term, the nonlinear robust feedback term, and the neural network fitting term; and These are the trajectory tracking error and its derivative, respectively. , and These are the angle, desired angle, and desired angular velocity of a multi-degree-of-freedom hydraulic robotic arm; It is a type of sliding modulus; This is the feedback gain matrix; For velocity tracking modulus; For thrust tracking error; and These represent the output thrust and the desired output thrust of the joint hydraulic cylinders of a multi-degree-of-freedom hydraulic robotic arm, respectively. For discontinuous sign functions, This is to address the nonlinear friction term using the Lagrange mean value theorem; For deterministic functions, As an intermediate auxiliary variable, t For time, These are preset approximation coefficients; and These represent the supply flow rates of the forward and return circuits of the cylinders in a multi-degree-of-freedom hydraulic robotic arm, respectively. and These are the constant current gain coefficient matrices for the forward and return loops of the cylinder, respectively. and These are the static mapping functions for the forward and return loops of the cylinder, respectively. and These are the intracavity pressures of the forward and return circuits of the cylinder, respectively.

[0016] System data includes trajectory tracking error, sliding modulus, thrust tracking error, desired angle and desired angular velocity of the multi-degree-of-freedom hydraulic manipulator, and intracavity pressure of the forward and return loops of the cylinder.

[0017] The virtual control flow Expected compensation items Linear feedback term Nonlinear robust feedback term Backstep compensation item and neural network fitting terms Specifically as follows:

[0018] in, This is a feedforward compensation term; Here, T is the second signal matrix, and T is the transpose. and These are the second parameter matrix and its estimated value, respectively; Effective bulk modulus; It is a unit column vector; for t The nominal value of the aggregate uncertainty of the flow at any given moment; and These are the flow linear feedback gain matrix and the flow nonlinear robust feedback gain matrix, respectively; and These are the balance coefficients for the second and third dimensions, respectively; and These are the neural network fitting term and input vector for the virtual control flow part of the radial basis function neural network (RBFNN), respectively.

[0019] The virtual control torque Expected compensation items Linear feedback term Nonlinear robust feedback term and neural network fitting terms Specifically as follows:

[0020] in, The first signal matrix, For the first ideal signal matrix, the desired signal is used to replace the measured signal; and These are the first parameter matrix and its estimated value, respectively; Let be the inertia matrix, and be a symmetric positive definite matrix; For velocity tracking modulus The derivative; For Coriolis torque and centrifugal torque; It is a unit column vector; and These are the viscosity and the Coulomb friction coefficient, respectively; for t The nominal value of the modeling error at any given time. The modeling error includes modeling uncertainty and parameter uncertainty. and These are the torque linear feedback gain matrix and the torque nonlinear robust feedback gain matrix, respectively; and Let be the neural network fitting term and input vector of the expected output torque part of the radial basis function neural network RBFNN, respectively.

[0021] In the second step, the system data of the multi-degree-of-freedom hydraulic manipulator is normalized and then clustered using the K-means++ clustering algorithm to obtain the center vector and width parameter. These are then input into a radial basis function neural network (RBFNN) for offline optimization of the structural parameters. The RBFNN is used to approximate the uncertainties remaining in the control. Each item in the system data is normalized and then clustered to select one or more cluster centers as the center vector of the neural network. The width parameter is calculated based on the cluster distribution, thereby solving the local optimum problem caused by random initialization and improving approximation accuracy and computational efficiency.

[0022] In the second step, the online adaptive law for the parameters of the Radial Basis Function Neural Network (RBFNN) is as follows:

[0023] in, and These are the weight vector estimates for the desired output torque component and the virtual control flow component, respectively. and These are the derivatives of the weight vector estimates for the desired output torque and the virtual control flow, respectively, i.e., the online adaptive law of parameters; For the first i A saturation function with a limited rate of change. and The preset maximum update rate for the weight vector estimates of the expected output torque and virtual control flow components, respectively; For the first i Discontinuous projection functions; For the first i Adaptive law for each intrinsic parameter; For the first i +1 update gain matrix; For the first i One Gaussian function; and These are respectively the sliding modulus and the thrust tracking error; For the first i One correction factor.

[0024] This invention proposes an optimized neural network-assisted adaptive robust control framework to achieve high-precision motion control of a multi-degree-of-freedom hydraulic manipulator under conditions of parameter uncertainty. A backstepping control method is systematically employed to handle the higher-order coupled dynamics of the system. The core contribution is a hybrid compensation strategy: an RBFNN with structure optimized using the K-means++ algorithm compensates for complex unmodeled dynamics, while integrating correction terms and expected compensation concepts to ensure robustness against parameter drift and sensor noise. Rigorous theoretical analysis is conducted to establish the asymptotic tracking performance of the closed-loop system. Comparative experimental results on a multi-degree-of-freedom hydraulic manipulator verify the effectiveness of the proposed controller and demonstrate that it achieves better tracking accuracy than the baseline control strategy.

[0025] The beneficial effects of this invention are: This invention utilizes the K-means++ algorithm to offline optimize the node centers and widths of an RBFNN. Compared to traditional random initialization methods, it achieves higher approximation accuracy with fewer nodes, significantly reducing the online computational load. Desired signal compensation enhances noise resistance: by replacing the measured signal with the desired trajectory signal in the model compensation term, the path of sensor noise amplification through the controller is effectively cut off, eliminating noise interference from velocity differences and improving system robustness. An adaptive law with a correction term ensures the boundedness and convergence of the neural network weights. Experimental results show that this method can reduce the root mean square error (RMSE) of trajectory tracking by more than 36%, effectively suppressing the "stick-slip" phenomenon during commutation. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the overall control framework of the method of the present invention; Figure 2 This is a comparison chart of the tracking performance of the forearm joint in this invention; Figure 3 This is a partially enlarged view comparing the tracking performance of the forearm joint in this invention; Figure 4 This is a comparison chart of the tracking performance of the wrist joint in this invention; Figure 5 This is a magnified view of the wrist joint tracking performance comparison in this invention; Figure 6 This is a comparison diagram of the expected output torque and voltage output of the forearm joint in this invention, wherein, Figure 6 (a) is the output thrust curve of the C-3 controller. Figure 6 (b) is the output thrust curve of the C-4 controller. Figure 6 (c) is the output voltage curve of the C-3 controller. Figure 6 (d) is the output voltage curve of the C-4 controller; Figure 7 This is a comparison diagram of the expected output torque and voltage output of the wrist joint in this invention, wherein, Figure 7 (a) is the output thrust curve of the C-3 controller. Figure 7 (b) is the output thrust curve of the C-4 controller. Figure 7 (c) is the output voltage curve of the C-3 controller. Figure 7 (d) is the output voltage curve of the C-4 controller. Detailed Implementation

[0027] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0028] like Figure 1 As shown, the adaptive robust control method for hydraulic robotic arms based on network structure optimization of the present invention is as follows: The first step is to design an adaptive robust controller based on the dynamic model of the multi-degree-of-freedom hydraulic manipulator using the backstepping method. The dynamic model of the multi-degree-of-freedom hydraulic manipulator includes parameter uncertainties, uncertain nonlinearities, and unmodeled dynamics. The specific dynamic model of the multi-degree-of-freedom hydraulic manipulator is as follows:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] in, It is the gravitational torque vector. ; For the joint angular acceleration of a multi-degree-of-freedom hydraulic robotic arm, ; The output torque of the hydraulic cylinders acting on the joints of a multi-degree-of-freedom hydraulic robotic arm. ; The frictional torque acting on the joint. ; For non-singular joint Jacobian matrices, For the first iThe non-singular joint Jacobian matrix of each joint; and These are the areas of the forward and return circuits of the cylinder, respectively. , ; and The first i The length of the triangle edge of the forward and return circuits of the cylinder of each joint; q i For the first i Each joint angle; and These are cylinder displacement and cylinder speed, respectively. and These are the volumes of the cylinder head and rod end chambers, respectively. , ; and These are the derivatives of the intracavity pressures in the forward and return circuits of the cylinder, respectively. , ; This is the oil leakage coefficient. ; and They are respectively t The flow rate of the forward and return loops of the cylinder is uncertain and nonlinear.

[0035] The adaptive robust controller obtains nonlinear robust feedback terms and basic control terms for torque and flow based on the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. These terms, together with the neural network fitting terms output by the radial basis function neural network (RBFNN), are used to obtain the virtual control torque and the desired output flow, thereby obtaining the desired output flow of the multi-degree-of-freedom hydraulic manipulator.

[0036] The adaptive robust controller is as follows:

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] in, For the control input voltage of a multi-degree-of-freedom hydraulic robotic arm, ; It is a statically mapped voltage function; , , , , and These are, respectively, virtual control flow and its expected compensation term, linear feedback term, nonlinear robust feedback term, backstepping compensation term, and neural network fitting term; , , , and These are, respectively, the virtual control torque and its expected compensation term, the linear feedback term, the nonlinear robust feedback term, and the neural network fitting term; and These are the trajectory tracking error and its derivative, respectively. , and These are the angle, desired angle, and desired angular velocity of a multi-degree-of-freedom hydraulic robotic arm; It is a type of sliding modulus; For the feedback gain matrix, , n This refers to the number of joints in the robotic arm. For velocity tracking modulus; For thrust tracking error; and These represent the output thrust and the desired output thrust of the joint hydraulic cylinders in a multi-degree-of-freedom hydraulic robotic arm, respectively. , ; For discontinuous sign functions, To handle the nonlinear friction term using Lagrange's mean value theorem , The vector to be processed; For deterministic functions, , As an intermediate auxiliary variable, t For time, These are preset approximation coefficients; and These represent the supply flow rates of the forward and return circuits of the cylinders in a multi-degree-of-freedom hydraulic robotic arm, respectively. , ; and These are the constant current gain coefficient matrices for the forward and return loops of the cylinder, respectively. and ; and These are the static mapping functions for the forward and return loops of the cylinder, respectively. , ; and These are the intracavity pressures of the forward and return circuits of the cylinder, respectively. , .

[0044] System data includes trajectory tracking error, sliding modulus, thrust tracking error, desired angle and desired angular velocity of the multi-degree-of-freedom hydraulic manipulator, and intracavity pressure of the forward and return loops of the cylinder.

[0045] Virtual control flow Expected compensation items Linear feedback term Nonlinear robust feedback term Backstep compensation item and neural network fitting terms Specifically as follows:

[0046]

[0047] in, This is a feedforward compensation term; Here, T is the second signal matrix, and T is the transpose. and These are the second parameter matrix and its estimated value, respectively; For effective bulk modulus, ; It is a unit column vector; for t The nominal value of the aggregate uncertainty of the flow at any given moment; and These are the flow linear feedback gain matrix and the flow nonlinear robust feedback gain matrix, respectively. , ; and These are the balance coefficients for the second and third dimensions, respectively; and These are the neural network fitting term and input vector for the virtual control flow part of the radial basis function neural network (RBFNN), respectively.

[0048] Virtual control torque Expected compensation items Linear feedback term Nonlinear robust feedback term and neural network fitting terms Specifically as follows:

[0049] in, The first signal matrix, For the first ideal signal matrix, the desired signal is used to replace the measured signal; and These are the first parameter matrix and its estimated value, respectively; Let be the inertia matrix, and be a symmetric positive definite matrix. ; For velocity tracking modulus The derivative; For Coriolis torque and centrifugal torque; It is a unit column vector; and These are the viscosity and the Coulomb friction coefficient, respectively. , ; for t The nominal value of the modeling error at any given time. Modeling errors include modeling uncertainty and parameter uncertainty; and These are the torque linear feedback gain matrix and the torque nonlinear robust feedback gain matrix, respectively. , ; and Let be the neural network fitting term and input vector of the expected output torque part of the radial basis function neural network RBFNN, respectively.

[0050] In the design of the adaptive robust controller, a regression matrix based on the desired trajectory signal (desired angle, desired angular velocity) is constructed to replace the traditional measured feedback signal, thereby avoiding differential amplification of the noise signal. Simultaneously, the optimized RBFNN is embedded into the controller to compensate for unmodeled dynamics online, and an adaptive law with correction terms and projection mapping is designed to update the weights and prevent parameter drift.

[0051] The second step involves acquiring system data of a multi-degree-of-freedom hydraulic manipulator, performing clustering optimization to obtain the center vector and width parameters as inputs to a radial basis function neural network (RBFNN), and designing an online adaptive law for the parameters of the RBFNN.

[0052] After normalizing the system data of the multi-degree-of-freedom hydraulic manipulator, K-means++ clustering algorithm is used for cluster optimization to obtain the center vector and width parameter. Then, the data is input into the radial basis function neural network (RBFNN) for offline optimization of the structural parameters. The RBFNN is used to approximate the uncertainty of the control residue. Each item in the system data is normalized and then clustered for optimization. One or more cluster centers are selected as the center vector of the neural network, and the width parameter is calculated according to the cluster distribution. This solves the local optimum problem caused by random initialization and improves the approximation accuracy and computational efficiency.

[0053] The output model of the Radial Basis Function Neural Network (RBFNN) is as follows:

[0054]

[0055]

[0056]

[0057] in, and These are the weight vector estimates for the desired output torque component and the virtual control flow component, respectively. and The network's first k The output vector of the Gaussian function and its... j Each component form; It is a 2-norm; The center vectors selected by the K-means++ algorithm. , j For the hidden layer of the network j 1 node k For the first k The output of one neural network; For the first k The width parameter corresponding to each Gaussian function .

[0058] The system data is used as a sample set and Z-score normalized. The first cluster center is randomly selected from the normalized data. For each data point in the sample set, its distance to the currently selected cluster center is calculated, and the next cluster center is selected with a probability proportional to the square of the distance, until a cluster center is selected. 1. Draw 1 cluster center; use the K-means++ algorithm to iteratively update the cluster centers until convergence, and obtain the final center vector. The width parameter of the Gaussian function is calculated based on the distance between the final cluster centers. .

[0059] The online adaptive law of design parameters updates the weight vector estimates of the desired output torque and virtual control flow components.

[0060] The online adaptive law for the parameters of the Radial Basis Function Neural Network (RBFNN) is as follows:

[0061] in, and These are the weight vector estimates for the desired output torque component and the virtual control flow component, respectively. and These are the derivatives of the weight vector estimates for the desired output torque and the virtual control flow, respectively, i.e., the online adaptive law of parameters; For the first i A saturation function with a limited rate of change. and The preset maximum update rate for the weight vector estimates of the expected output torque and virtual control flow components, respectively; For the first i Discontinuous projection functions; For the first i Adaptive law for each intrinsic parameter; For the first i +1 update gain matrix; For the first i One Gaussian function; and These are respectively the sliding modulus and the thrust tracking error; For the first i One correction factor.

[0062] The third step involves inputting the system data, along with the center vector and width parameters, into the Radial Basis Function Neural Network (RBFNN). The estimated weight vector of the RBFNN is then updated using an online adaptive law. The RBFNN processes and outputs a neural network fitting term, which is then input into an adaptive robust controller along with the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. After processing, the controller outputs a control input voltage. This control input voltage is then statically mapped to obtain the valve control voltage, which in turn controls the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator.

[0063] The specific design of the method in this invention involves online adaptive parameter updating of the radial basis function neural network embedded in the adaptive robust controller. This is achieved using a pre-designed weight update law with correction terms and projection mapping, based on the real-time calculated joint position tracking error. Torque tracking error and the pressure in each chamber of the hydraulic robotic arm cylinder. Update the weight estimates of the first layer of the neural network used to approximate the unmodeled dynamics of the dynamic model. And the weight estimates of the second-layer neural network used to approximate the uncertainty of flow dynamics. This ensures the bounded convergence of the parameter estimation. Subsequently, the adaptive robust controller calculates the desired output torque. (Including basic control flow) Linear robust feedback term and neural network compensation terms ) and virtual control flow (Including basic control flow) Linear robust feedback term and neural network compensation terms Based on the pressure-flow characteristics of the hydraulic valve, a static mapping is performed to calculate the valve port control voltage command corresponding to each joint hydraulic servo valve. This, in turn, drives the hydraulic valves of the multi-degree-of-freedom hydraulic robotic arm to actuate, thereby achieving the desired trajectory. High-precision closed-loop tracking.

[0064] In a specific implementation, the control method of this invention was applied to a hydraulic robotic arm for testing. To demonstrate the effectiveness of the method, it was validated on the wrist and rod-like joints, and trajectories incorporating various dynamic information were designed, such as... Figure 2 As shown, the overall asymptotic tracking performance of the controller is verified through static, constant angular velocity, constant angular acceleration, and constant angular jerk. The following four controllers are selected for comparative analysis (the controller gain has been adjusted to the limit edge until slight jitter appears): C-4: The controller of this invention. Parameter selection. , , , , , , , , , The number of hidden layer nodes used in RBFNN is set to 5.

[0065] C-3: A controller with adaptive model compensation, where the parameter settings are consistent with C-4. Compared to C-4, it updates the parameter estimates using an adaptive gradient descent law when handling uncertainties. as follows:

[0066] in, and For adaptive gain.

[0067] C-2: A controller with deterministic model compensation. Compared to C-3, this controller keeps other parameters constant but does not update the estimated parameters, i.e. .

[0068] C-1: Sliding mode controller. Compared to C-2, the estimated parameter is equal to 0, i.e. .

[0069] Regarding control effectiveness, the following metrics are used for comparison: maximum tracking error. Normalized performance index , For the maximum tracking error, the root mean square error (RMSE) and integral absolute error (IAE) are as follows: ,

[0070] in, T For the integration period; e This represents the error at each time point within the period.

[0071] like Figure 2 and Figure 4 As shown, the tracking trajectories and error distributions for the forearm and wrist joints are depicted, respectively. It is evident that the non-model-based controller C-1 exhibits the most significant tracking error. Although its feedback gain is tuned to its stability limit, it fails to effectively suppress nonlinearity due to the lack of dynamic compensation, thus preventing further gain increases without inducing oscillations. In contrast, C-2, by incorporating a model-based feedforward compensation term (i.e., ... This resulted in a substantial improvement in tracking accuracy. This effectively mitigated errors during dynamic transitions. However, because physical parameters cannot be identified offline with perfect accuracy (i.e., ... Therefore, C-2 suffers from residual steady-state error due to parameter mismatch. C-3 addresses this limitation by employing an adaptive law based on gradient descent to estimate uncertain parameters online. While this strategy further reduces tracking error compared to C-2, its performance is limited by the adaptive mechanism itself: since the update law is driven solely by tracking error, it is susceptible to parameter drift or slow adaptation, especially in the presence of sensor noise or with small errors. Table 1 shows a numerical comparison of the tracking results for different controllers.

[0072] Table 1

[0073] Although the overall error indices summarized in Table 1 demonstrate the statistical advantages of the method of this invention, Figure 3 and Figure 5The magnified view in the image provides important insights into controller performance under critical dynamic conditions. Specifically, such as... Figure 3 As shown, the tracking performance of the forearm joint during the dynamic change phase (approximately t = 18.3 seconds) is highlighted. At this zero-velocity crossover point, the hydraulic manipulator typically suffers from severe nonlinearity caused by valve dead zones and friction. It can be observed that the error curve of C-3 exhibits significant fluctuations (chattering) during this transition, indicating that traditional gradient descent-based adaptive laws struggle to quickly compensate for rapidly changing frictional dynamics. In contrast, the error curve of the proposed C-4 remains smooth and bounded to near zero. This confirms that the optimized RBFNN effectively captures local inverse dynamics and significantly mitigates the impact of "stick-slip" during directional changes. Figure 5 As shown, the magnified region (ranging from 13.5 seconds to 15.5 seconds) details the wrist joint response during the fast trajectory tracking phase. C-1 and C-2 exhibit significant steady-state errors and phase lag due to a lack of effective compensation for unmodeled uncertainties. While C-3 reduces the steady-state error, its convergence is slower when stabilizing to the desired trajectory. Conversely, C-4 demonstrates superior transient performance with faster convergence and negligible overshoot. This improvement is attributed to the K-Means++ algorithm, which optimizes the distribution of neuron centers based on the system's workspace, thus ensuring higher approximation accuracy for the unmodeled residuals.

[0074] Table 1 quantitatively validates this enhanced performance. The RMSE metrics calculated across the entire multi-cycle trajectory show a substantial improvement. Compared to the C-3 (ARC) controller, the proposed C-4 method achieves a 36.7% reduction in forearm joint RMSE (from 0.1967 degrees to 0.1246 degrees) and a 40.6% reduction in wrist joint RMSE (from 0.2694 degrees to 0.1601 degrees). The significant improvement in tracking accuracy during average metrics and key dynamic transitions underscores the practical superiority of the optimized neural network-assisted method. Ultimately, C-4 achieves the most accurate tracking performance and the best error suppression among all controllers. Tracking results demonstrate that C-4 is suitable for scenarios requiring precise control and adaptation.

[0075] like Figure 6 of (a) Figure 6 of (b) Figure 6 (c) Figure 6 of (d), Figure 7 of (a) Figure 7 of (b) Figure 7 (c) and Figure 7 Figure (d) shows the control outputs of the forearm and wrist joints under C-3 and C-4, respectively. From top to bottom, the figure shows the desired output torque and the neural network compensation term. and output voltage It can be seen that, compared with C-3, C-4 exhibits smaller output fluctuations and greater stability. In particular, the C-3 method shows larger fluctuations, especially in thrust control, where its performance is significantly worse. This highlights the limitations of C-3 in handling rapid dynamic changes and effectively compensating for uncertainties.

[0076] Regarding output voltage, both methods exhibit comparable performance under regular time fluctuations. However, the output voltage of C-4 is slightly lower than that of C-3. More importantly, C-4 demonstrates superior ability to suppress voltage transients near peak values ​​and during voltage abrupt changes (e.g., voltage transients observed at 8 and 16 seconds). This enhanced performance further confirms the lower tracking error of C-4 during dynamic transitions. Overall, the C-4 method represents a significant improvement over the C-3 method in terms of dynamic response, tracking accuracy, and robustness. These advantages make C-4 a more efficient and reliable control strategy, particularly in applications requiring high accuracy and adaptability.

[0077] This invention utilizes the K-means++ algorithm to offline optimize the node centers and widths of an RBFNN. Compared to traditional random initialization methods, it achieves higher approximation accuracy with fewer nodes, significantly reducing the online computational load. Desired signal compensation enhances noise resistance: by replacing the measured signal with the desired trajectory signal in the model compensation term, the path of sensor noise amplification through the controller is effectively cut off, eliminating noise interference from velocity differences and improving system robustness. An adaptive law with a correction term ensures the boundedness and convergence of the neural network weights. Experimental results show that this method can reduce the root mean square error (RMSE) of trajectory tracking by more than 36%, effectively suppressing the "stick-slip" phenomenon during commutation.

[0078] In summary, considering the inherent high-order nonlinearity, parameter uncertainty, and the severe challenges posed by sensor noise to precise control in multi-degree-of-freedom hydraulic manipulators, this invention proposes an adaptive robust control method based on network structure optimization. By introducing the K-means++ clustering algorithm to perform data-driven offline optimization of the center and width parameters of the RBFNN, this invention accurately approximates the unmodeled dynamics (such as complex friction and leakage) in the system, significantly improving approximation accuracy while maintaining computational efficiency. Furthermore, this invention creatively uses the desired trajectory signal to replace the measured state signal in the controller design to construct the regression matrix, effectively cutting off the path of noise amplification caused by differential calculations. Combined with an adaptive law with a correction term, this greatly enhances the robustness of the closed-loop system. Finally, comparative experiments on a multi-degree-of-freedom hydraulic manipulator demonstrate that this method significantly reduces trajectory tracking error (RMSE reduction of over 36%) compared to traditional adaptive control strategies and successfully eliminates "stick-slip" oscillations during commutation, achieving high-precision motion control under complex working conditions.

[0079] The above content is merely a technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. An adaptive robust control method for a hydraulic robotic arm based on network structure optimization, characterized in that, include: The first step is to design an adaptive robust controller based on the dynamic model of a multi-degree-of-freedom hydraulic manipulator using the backstepping method; The second step is to acquire the system data of the multi-degree-of-freedom hydraulic manipulator, perform clustering optimization to obtain the center vector and width parameters as inputs to the radial basis function neural network (RBFNN), and design the online adaptive law for the parameters of the RBFNN. The third step involves inputting the system data, along with the center vector and width parameters, into the Radial Basis Function Neural Network (RBFNN). The estimated weight vector of the RBFNN is then updated using an online adaptive law. The RBFNN processes and outputs a neural network fitting term, which is then input into an adaptive robust controller along with the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. After processing, the controller outputs a control input voltage. This control input voltage is then statically mapped to obtain the valve control voltage, which in turn controls the hydraulic valve of the multi-degree-of-freedom hydraulic manipulator.

2. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 1, characterized in that: In the first step, the adaptive robust controller obtains nonlinear robust feedback terms and basic control terms for torque and flow rate based on the trajectory tracking error of the multi-degree-of-freedom hydraulic manipulator. These terms, together with the neural network fitting terms output by the radial basis function neural network (RBFNN), are used to obtain the virtual control torque and the desired output flow rate, thereby obtaining the desired output flow rate of the multi-degree-of-freedom hydraulic manipulator.

3. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 2, characterized in that: The adaptive robust controller is as follows: in, The control input voltage for a multi-degree-of-freedom hydraulic robotic arm; It is a statically mapped voltage function; , , , , and These are, respectively, virtual control flow and its expected compensation term, linear feedback term, nonlinear robust feedback term, backstepping compensation term, and neural network fitting term; , , , and These are, respectively, the virtual control torque and its expected compensation term, the linear feedback term, the nonlinear robust feedback term, and the neural network fitting term; and These are the trajectory tracking error and its derivative, respectively. , and These are the angle, desired angle, and desired angular velocity of a multi-degree-of-freedom hydraulic robotic arm; It is a type of sliding modulus; This is the feedback gain matrix; For velocity tracking modulus; For thrust tracking error; and These represent the output thrust and the desired output thrust of the joint hydraulic cylinders of a multi-degree-of-freedom hydraulic robotic arm, respectively. For discontinuous sign functions, This is to address the nonlinear friction term using Lagrange's mean value theorem; For deterministic functions, As an intermediate auxiliary variable, t For time, These are preset approximation coefficients; and These represent the supply flow rates of the forward and return circuits of the cylinders in a multi-degree-of-freedom hydraulic robotic arm, respectively. and These are the constant current gain coefficient matrices for the forward and return loops of the cylinder, respectively. and These are the static mapping functions for the forward and return loops of the cylinder, respectively. and These are the intracavity pressures of the forward and return circuits of the cylinder, respectively. System data includes trajectory tracking error, sliding modulus, thrust tracking error, desired angle and desired angular velocity of the multi-degree-of-freedom hydraulic manipulator, and intracavity pressure of the forward and return loops of the cylinder.

4. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 3, characterized in that: The virtual control flow Expected compensation items Linear feedback term Nonlinear robust feedback term Backstep compensation item and neural network fitting terms Specifically as follows: in, This is a feedforward compensation term; Here, T is the second signal matrix, and T is the transpose. and These are the second parameter matrix and its estimated value, respectively; Effective bulk modulus; It is a unit column vector; for t The nominal value of the aggregate uncertainty of the flow at any given moment; and These are the flow linear feedback gain matrix and the flow nonlinear robust feedback gain matrix, respectively; and These are the balance coefficients for the second and third dimensions, respectively; and These are the neural network fitting term and input vector for the virtual control flow part of the radial basis function neural network (RBFNN), respectively.

5. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 3, characterized in that: The virtual control torque Expected compensation items Linear feedback term Nonlinear robust feedback term and neural network fitting terms Specifically as follows: in, The first signal matrix, This is the first ideal signal matrix; and These are the first parameter matrix and its estimated value, respectively; The inertia matrix; For velocity tracking modulus The derivative; For Coriolis torque and centrifugal torque; It is a unit column vector; and These are the viscosity and the Coulomb friction coefficient, respectively; for t The nominal value of the modeling error at any given time; and These are the torque linear feedback gain matrix and the torque nonlinear robust feedback gain matrix, respectively; and Let be the neural network fitting term and input vector of the expected output torque part of the radial basis function neural network RBFNN, respectively.

6. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 1, characterized in that: In the second step, the system data of the multi-degree-of-freedom hydraulic manipulator is normalized and then clustered using the K-means++ clustering algorithm to obtain the center vector and width parameters. These parameters are then input into the radial basis function neural network (RBFNN) for offline optimization.

7. The adaptive robust control method for a hydraulic robotic arm based on network structure optimization according to claim 1, characterized in that: In the second step, the online adaptive law for the parameters of the Radial Basis Function Neural Network (RBFNN) is as follows: in, and These are the weight vector estimates for the desired output torque component and the virtual control flow component, respectively. and These are the derivatives of the weight vector estimates for the desired output torque and the virtual control flow, respectively. For the first i A saturation function with a limited rate of change. and The preset maximum update rate for the weight vector estimates of the expected output torque and virtual control flow components, respectively; For the first i Discontinuous projection functions; For the first i Adaptive law for each intrinsic parameter; For the first i +1 update gain matrix; For the first i One Gaussian function; and These are respectively the sliding modulus and the thrust tracking error; For the first i One correction factor.

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