Self-adaptive robust control method for finite time convergence of hydraulic mechanical arm under unknown load

Abstract

The invention discloses a finite time convergence adaptive robust control method for a hydraulic mechanical arm under an unknown load. The method comprises the steps that a system dynamics model of the hydraulic mechanical arm is reconstructed through a generalized momentum method, and a finite time convergence adaptive law and a nonlinear controller are designed; the state information of the mechanical arm is input into the finite time convergence self-adaption law in real time, the corrected self-adaption gain updating law is output after processing so as to update the self-adaption gain in the nonlinear controller in real time, meanwhile, the expected track and the expected output thrust of the mechanical arm are input into the nonlinear controller, virtual control flow is output after processing, and therefore the self-adaption gain in the nonlinear controller is updated in real time. And after nonlinear flow mapping is conducted, valve port control voltage is obtained, and then a proportional control valve of the mechanical arm is controlled. On the basis of Lyapunov analysis, finite time convergence of parameter estimation and asymptotic convergence of trajectory tracking errors of the method are strictly proved, and the method shows excellent performance in the aspects of tracking precision and load estimation accuracy of a hydraulic mechanical arm platform.

Description

Technical Field

[0001] This invention relates to a hydraulic robotic arm control method, specifically to a finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load. Background Technology

[0002] Hydraulic robotic arms are widely used in heavy-duty tasks such as construction, mining, and marine operations due to their robustness in high power density and harsh environments. Compared to electric drives, hydraulic drives maintain force output capability under dust, impact, and temperature variations, making them ideal for demanding outdoor applications. However, as tasks become increasingly complex and precise, designing high-performance controllers for hydraulic robotic arms with high nonlinearity, parameter uncertainty, and joint coupling remains challenging. Furthermore, reliable load estimation is equally crucial for safe operation and adaptive force control. The simultaneous presence of nonlinear control challenges and uncertain load dynamics demands controllers capable of both precise motion control and accurate real-time parameter estimation. Most existing methods only guarantee asymptotic or exponential convergence of estimation errors. This limitation has spurred extensive research over the past few decades on finite-time stability and stabilization, establishing rigorous frameworks through Lyapunov methods and extending them to various types of uncertain nonlinear systems. Finite-time adaptive estimation can ensure rapid convergence within a finite time and exhibits stronger robustness than exponential stability. Finite-time adaptive estimation is particularly important for load estimation, as it enables fast and accurate convergence, which is crucial for heavy-load operations where inaccurate or delayed load estimation can jeopardize performance and safety. Summary of the Invention

[0003] To address the problems existing in the background art, the present invention provides a finite-time convergence adaptive robust control method for hydraulic robotic arms under unknown loads.

[0004] The technical solution adopted in this invention is: The present invention provides a finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load, comprising: The first step is to reconstruct the system dynamics model of the multi-degree-of-freedom hydraulic manipulator using the generalized momentum method. Based on the reconstructed system dynamics model, a finite-time convergent adaptive law based on generalized momentum for unknown loads and a nonlinear controller based on the backstepping method for high-performance trajectory tracking are designed.

[0005] The second step is to input the state information of the multi-degree-of-freedom hydraulic manipulator into the finite-time convergence adaptive law in real time, and then output the corrected adaptive gain update law after processing.

[0006] The third step involves updating the adaptive gain in the nonlinear controller in real time based on the modified adaptive gain update law. At the same time, the desired trajectory and desired output thrust of the multi-degree-of-freedom hydraulic manipulator are input into the nonlinear controller. After processing, the virtual control flow is output. After nonlinear flow mapping, the valve port control voltage is obtained, and then the proportional control valve of the multi-degree-of-freedom hydraulic manipulator is controlled.

[0007] In the first step, the reconstructed system dynamics model is as follows:

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[0014] in, and These are the system dynamics model and its differential of a multi-degree-of-freedom hydraulic manipulator reconstructed using the generalized momentum method; and These are the momentum term and load momentum coefficient matrix of the multi-degree-of-freedom hydraulic manipulator, respectively. and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; For an unknown load on a multi-degree-of-freedom hydraulic robotic arm; and These are the inertia matrix of the multi-degree-of-freedom hydraulic manipulator and the coefficient matrix of the inertia matrix components caused by the load, respectively. and These are the known dynamics and estimated friction terms and load-related dynamics terms of a multi-degree-of-freedom hydraulic manipulator, respectively. Friction parameter vector of the robotic arm The estimated value; For unknown disturbances in a multi-degree-of-freedom hydraulic robotic arm; t For time; For non-singular joint Jacobian matrices; To output thrust for the hydraulic cylinder; and These are the gravity term and the coefficient vector of the gravity term caused by the load for the multi-degree-of-freedom hydraulic manipulator, respectively. This is the transpose of the matrix; and These are the Coriolis matrix of the multi-degree-of-freedom hydraulic manipulator and the coefficient matrix of the Coriolis matrix components caused by the load, respectively. This is the regression matrix; It is a first-order low-pass filter. To pass the material through a first-order filter, a low-pass filter is first applied, and then the time derivative is taken. This represents the uncertainty and disturbance terms after filtering.

[0015] In the first step described above, the finite-time convergent adaptive law is as follows:

[0016] in, and These are the adaptive gain and the corrected adaptive gain update law, respectively. Forgetting factor is a normal number; This is the adaptive gain scaling factor; This is the gain attenuation coefficient; It is an n-dimensional identity matrix; and These are the auxiliary matrix and the auxiliary vector, respectively. t 0 represents the initial time. For generalized joint torque; This is the filtered load regression matrix; This is the transpose of the matrix; and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error, Update the load quality estimation law; For error integral variables; It is the Euclidean norm; The filtered uncertainty and disturbance terms; This is the positive gain adjustment parameter.

[0017] The status information of a multi-degree-of-freedom hydraulic robotic arm includes the joint positions of the multi-degree-of-freedom hydraulic robotic arm. and speed The pressure in the rodless chamber of the hydraulic cylinder of a multi-degree-of-freedom hydraulic robotic arm. Pressure in the rod chamber The area of ​​the rodless and rod chambers of the hydraulic cylinder and .

[0018] In the first step, the nonlinear controller is specifically as follows:

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[0027] in, , and These are respectively the virtual control flow and its adaptive feedforward and robust feedback components. For the first adaptive feedforward term based on the model, To compensate for unmodeled dynamics and disturbances at the joint level, a first fast dynamic compensation term is used. For the first linear feedback term, This is the first nonlinear robust feedback term; This is the area-to-volume ratio coefficient of the hydraulic cylinder; For flow regression vector; For flow parameter vector The estimate; This represents the analytical part of the desired thrust derivative; The positive definite symmetric matrix for the feedback gain of the hydraulic layer. The nonlinear feedback gain of the positive definite symmetric matrix hydraulic layer is designed based on the upper bound of uncertainty. For thrust tracking error; and These are the adaptive robust terms and their update law, respectively. The effective bulk modulus; The estimation error of the flow parameter vector; and These are the desired output thrust and its derivative, respectively. and These are the friction parameter vectors of a multi-degree-of-freedom hydraulic robotic arm. The estimated value and its derivative; This is an estimate of the acceleration of a multi-degree-of-freedom hydraulic manipulator; for t Momentary flow uncertainty and disturbances; This is the first preset limit; The second positive definite symmetric adaptive gain coefficient; This represents the upper limit of hydraulic disturbance. For hydraulic disturbance parameters, for t Momentary flow uncertainty and disturbance The upper bound of uncertainty; For position tracking error, For speed tracking error; For the desired trajectory; and These are the virtual control quantity and its derivative; It is a positive definite feedback gain matrix; For non-singular joint Jacobian matrices; For the desired thrust adaptive feedforward compensation part, This is a model-based second adaptive feedforward. To compensate for unmodeled dynamics and disturbances at the joint level, a second fast dynamic compensation term is used. For the desired thrust robust feedback part, This is the second linear feedback part. This is the second nonlinear robust feedback term; This is the load dynamics regression matrix; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error; The second derivative of the virtual control quantity; For the linear part of the feedback gain matrix, It is the positive definite matrix of the nonlinear robust feedback designed based on the upper bound of uncertainty; and These are the estimates of the uncertainty in modeling at the joint level and their derivatives, respectively. This is the second preset limit; The first positive definite symmetric adaptive gain parameter; This is the upper bound for the uncertainty of unknown perturbations. For unknown disturbance parameters; and These are the areas of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and These are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and They are respectivelyt The definitive nominal values ​​of the flow rates in the rodless and rod chambers of the hydraulic cylinder at all times.

[0028] This invention uses a given desired trajectory as input. The input is a model-based backstepping nonlinear controller, which follows a two-step design: first, it calculates the required desired output thrust based on the trajectory tracking error; second, it converts this thrust into a virtual control flow rate of the hydraulic system based on the hydraulic dynamics model. This flow rate signal passes through a nonlinear flow mapping module and is ultimately generated as the actual control voltage driving the hydraulic valve, thereby manipulating the hydraulic robotic arm to perform actions. The system runs an online parameter estimation loop in parallel to achieve adaptation to uncertainties such as unknown loads. Using real-time measured system information (such as joint position, velocity, and pressure) as input, a load dynamics model without acceleration terms is first reconstructed using the generalized momentum method. Based on this, the system constructs and updates a pair of auxiliary matrices online, which explicitly extract the parameter estimation error. This error information drives the core finite-time adaptive law, which ensures that the estimated load parameters converge quickly to the true value within a finite time. The "step size" or learning rate of the entire parameter update process is dynamically adjusted by a modified adaptive gain module to balance convergence speed and robustness. The high-precision parameter estimates derived online are fed back to the upper-level nonlinear controller in real time for accurate load compensation and model feedforward updates, thus forming a tightly integrated adaptive control closed loop. The actual motion output of the robotic arm is compared with the initial desired trajectory, and the resulting tracking error is continuously fed back to the controller input, enabling the entire system to simultaneously achieve high-precision trajectory tracking and fast and accurate online load identification.

[0029] The beneficial effects of this invention are: This invention proposes a finite-time convergent adaptive robust controller for a hydraulic manipulator. It combines a finite-time adaptive law based on generalized momentum for unknown loads with a two-layer robust control framework for high-performance trajectory tracking. The system dynamics are reconstructed using the generalized momentum method, and a regression term related to the load and excluding acceleration terms is extracted for parameter estimation. An auxiliary matrix is ​​constructed to extract parameter estimation error information, and a finite-time adaptive law is designed based on this. A two-layer control framework is proposed using backstepping techniques, where a fast dynamic compensation term accelerates the dynamic response speed, and a nonlinear robust feedback term weakens the influence of nonlinearity and external disturbances. This invention rigorously proves the finite-time convergence of parameter estimation and the asymptotic convergence of trajectory tracking errors using Lyapunov analysis. The proposed controller exhibits superior performance in terms of tracking accuracy and load estimation accuracy for the hydraulic manipulator platform. Attached Figure Description

[0030] Figure 1 This is a block diagram illustrating the principle of the motion controller of the present invention. Figure 2 This is a schematic diagram of the motion control experimental hardware platform of the method of the present invention; Figure 3 The graph shows the estimation results of the unknown load under four parameter estimation algorithms—finite-time convergence method, gradient descent method, recursive least squares method, and improved adaptive parameter estimation—in a specific implementation of this invention. Figure 4 This is a graph showing the estimation results of the finite-time convergence method under four different loads in a specific implementation of the present invention. Figure 4 (a) is the experimental curve for 7.5 kg. Figure 4 (b) is the experimental curve for 10 kg. Figure 4 (c) is the experimental curve for 12.5kg. Figure 4 (d) is the experimental curve for 15 kg; Figure 5 These are two target trajectories for joint 2 designed for experimental verification of control performance in the specific implementation of this invention. Figure 5 (a) is a graph of the sine trajectory. Figure 5 (b) is a point-to-point trajectory curve; Figure 6 This is a graph showing the single-joint trajectory tracking performance of different control methods under no-load conditions during a specific implementation of the present invention. Figure 7 This is a graph showing the single-joint trajectory tracking performance of different control methods under no-load conditions during a specific implementation of the present invention. Figure 8 This is a comparison curve of the tracking performance under no-load conditions when the controller proposed in this invention is in action during a specific implementation of this invention. Detailed Implementation

[0031] 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.

[0032] like Figure 1 As shown, the finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load of the present invention is as follows: The first step is to reconstruct the system dynamics model of the multi-degree-of-freedom hydraulic manipulator using the generalized momentum method. Based on the reconstructed system dynamics model, a finite-time convergent adaptive law based on generalized momentum for unknown loads and a nonlinear controller based on the backstepping method for high-performance trajectory tracking are designed.

[0033] The reconstructed system dynamics model is as follows:

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[0040] in, and These are the system dynamics model and its differential of a multi-degree-of-freedom hydraulic manipulator reconstructed using the generalized momentum method; and These are the momentum term and load momentum coefficient matrix of the multi-degree-of-freedom hydraulic manipulator, respectively. and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; For the unknown load of a multi-degree-of-freedom hydraulic robotic arm, ; and These are the inertia matrix of the multi-degree-of-freedom hydraulic manipulator and the coefficient matrix of the inertia matrix components caused by the load, respectively. and These are the known dynamics and estimated friction terms and load-related dynamics terms of a multi-degree-of-freedom hydraulic manipulator, respectively. Friction parameter vector of the robotic arm The estimated value; For unknown disturbances in a multi-degree-of-freedom hydraulic robotic arm; t For time; For non-singular joint Jacobian matrices; To output thrust for the hydraulic cylinder; and These are the gravity term and the coefficient vector of the gravity term caused by the load for the multi-degree-of-freedom hydraulic manipulator, respectively. This is the transpose of the matrix; and These are the Coriolis matrix of the multi-degree-of-freedom hydraulic manipulator and the coefficient matrix of the Coriolis matrix components caused by the load, respectively. This is the regression matrix; It is a first-order low-pass filter that performs low-pass filtering on the input signal to suppress high-frequency noise. To perform low-pass filtering on the input signal using a first-order filter, and then take the time derivative; This represents the uncertainty and disturbance terms after filtering.

[0041] The system dynamics model before reconstruction is as follows:

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[0061] in, , , and These are the inertia matrix, Coriolis term, gravity term, and friction torque of the multi-degree-of-freedom hydraulic manipulator, respectively. The acceleration of a multi-degree-of-freedom hydraulic robotic arm; , and These are the Lagrangian quantity, kinetic energy, and potential energy of the linkage in a multi-degree-of-freedom hydraulic manipulator, respectively. and These are viscous friction and Coulomb friction, respectively. and These are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. The effective bulk modulus; and The pressures of the rodless chamber of the hydraulic cylinder are respectively... Pressure in the rod chamber The derivative; and These are the areas of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and These are the displacement and speed of the hydraulic cylinder, respectively. and The flow rate is supplied to the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and They are respectively t The definitive nominal values ​​of the flow rates in the rodless and rod chambers of the hydraulic cylinder at any given time. and They are respectively t The error in the chambers of the rodless and rod-type hydraulic cylinder at any given time; and These are the constant flow gain coefficients for the forward and reverse loops, respectively; and These are the pressure-related flow functions for the rodless and rod-type chambers of the hydraulic cylinder, respectively. This refers to the valve port control voltage of the hydraulic valve. For the first i The pressure in the rodless chamber of a hydraulic cylinder. For the first i The pressure in the rod chamber of a hydraulic cylinder; For the first i The control voltage of the hydraulic valve port of each hydraulic cylinder; The oil supply pressure of the hydraulic pump. This refers to the return oil pressure of the hydraulic pump. This is the load dynamics regression matrix; The generalized joint torque is obtained by converting the thrust output by the hydraulic cylinder through the Jacobian. The derivative of the hydraulic cylinder's output thrust; This is the area-to-volume ratio coefficient of the hydraulic cylinder; This is the equivalent composite flow term; For flow regression vector; A vector of flow parameters; for t Momentary flow uncertainty and disturbances.

[0062] The finite-time convergent adaptive law is as follows:

[0064] in, and These are the adaptive gain and the corrected adaptive gain update law, respectively. To ensure and Bounded normal number forgetting factor; This is an adaptive gain scaling factor used to adjust the update rate; This is the gain attenuation coefficient; It is an n-dimensional identity matrix; and These are the auxiliary matrix and the auxiliary vector, respectively. t 0 represents the initial time. For generalized joint torque; This is the filtered load regression matrix; This is the transpose of the matrix; and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error, Update the load quality estimation law; For error integral variables; It is the Euclidean norm; The filtered uncertainty and disturbance terms; This is the positive gain adjustment parameter; It is an intermediate variable.

[0065] The status information of a multi-degree-of-freedom hydraulic robotic arm includes the joint positions of the multi-degree-of-freedom hydraulic robotic arm. and speed The pressure in the rodless chamber of the hydraulic cylinder of a multi-degree-of-freedom hydraulic robotic arm. Pressure in the rod chamber The area of ​​the rodless and rod chambers of the hydraulic cylinder and .

[0066] The nonlinear controller is as follows:

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[0084] in, , and These are respectively the virtual control flow and its adaptive feedforward and robust feedback components. For the first adaptive feedforward term based on the model, To compensate for unmodeled dynamics and disturbances at the joint level, a first fast dynamic compensation term is used. For the first linear feedback term, This is the first nonlinear robust feedback term; This is the area-to-volume ratio coefficient of the hydraulic cylinder; For flow regression vector; For flow parameter vector The estimate; This represents the analytical part of the desired thrust derivative; The positive definite symmetric matrix for the feedback gain of the hydraulic layer. The nonlinear feedback gain of the positive definite symmetric matrix hydraulic layer is designed based on the upper bound of uncertainty. For thrust tracking error; and These are the adaptive robust terms and their update law, respectively. The effective bulk modulus; The estimation error of the flow parameter vector; and These are the desired output thrust and its derivative, respectively. and These are the friction parameter vectors of a multi-degree-of-freedom hydraulic robotic arm. The estimated value and its derivative; This is an estimate of the acceleration of a multi-degree-of-freedom hydraulic manipulator; for t Momentary flow uncertainty and disturbances; and These are the low-frequency and high-frequency components of the uncertainty in hydraulic level modeling and the decomposition of estimation error. This is the first preset limit; The second positive definite symmetric adaptive gain coefficient; This represents the upper limit of hydraulic disturbance. Let be the hydraulic disturbance parameter, which is any parameter that is arbitrarily small and greater than 0. for t Momentary flow uncertainty and disturbance The upper bound of uncertainty; For position tracking error, For speed tracking error; For the desired trajectory; and These are the virtual control quantity and its derivative; It is a positive definite feedback gain matrix; Estimate the uncertainty for modeling the joint level; For non-singular joint Jacobian matrices; For the desired thrust adaptive feedforward compensation part, This is a model-based second adaptive feedforward. To compensate for unmodeled dynamics and disturbances at the joint level, a second fast dynamic compensation term is used. For the desired thrust robust feedback part, This is the second linear feedback part. This is the second nonlinear robust feedback term; This is the load dynamics regression matrix; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error; The second derivative of the virtual control quantity; For the linear part of the feedback gain matrix, It is the positive definite matrix of the nonlinear robust feedback designed based on the upper bound of uncertainty; and These are the estimates of the uncertainty in modeling at the joint level and their derivatives, respectively. and These are the low-frequency and high-frequency components of the uncertainty in joint-level modeling and the parameter estimation error, respectively. Friction parameter vector of a multi-degree-of-freedom hydraulic manipulator The estimation error; This is the second preset limit; The first positive definite symmetric adaptive gain parameter; This is the upper bound for the uncertainty of unknown perturbations. Unknown disturbances for multi-degree-of-freedom hydraulic robotic arms The upper bound of uncertainty For unknown disturbance parameters, It is any small parameter greater than 0; For the analytical part of the desired thrust derivative, This represents the non-analytical part of the desired thrust derivative; and These are the areas of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and These are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and They are respectively t The definitive nominal values ​​of the flow rates in the rodless and rod chambers of the hydraulic cylinder at all times.

[0085] The nonlinear controller integrates a fast dynamic compensation term and a nonlinear robust feedback term. The fast dynamic compensation term includes... and The fast dynamic compensation term accelerates the dynamic response speed, and the nonlinear robust feedback term includes and and The nonlinear robust feedback term weakens the effects of nonlinearity and external disturbances.

[0086] The second step is to input the state information of the multi-degree-of-freedom hydraulic manipulator into the finite-time convergence adaptive law in real time, and then output the corrected adaptive gain update law after processing.

[0087] The third step involves updating the adaptive gain in the nonlinear controller in real time based on the modified adaptive gain update law. At the same time, the desired trajectory and desired output thrust of the multi-degree-of-freedom hydraulic manipulator are input into the nonlinear controller. After processing, the virtual control flow is output. After nonlinear flow mapping, the valve port control voltage is obtained, and then the proportional control valve of the multi-degree-of-freedom hydraulic manipulator is controlled. Figure 1 In the system information, the information includes: joint position, joint velocity, hydraulic cylinder output thrust, hydraulic pump oil supply pressure, hydraulic cylinder displacement, and other robot arm sensor information required for constructing auxiliary vectors / matrices using the generalized momentum method.

[0088] like Figure 2 As shown, LabVIEW transmits control commands to the NI board, which then converts them and transmits them to the hydraulic robotic arm for control. The sensors send the sensor signals from the hydraulic robotic arm to the NI board, which converts them and transmits the system status back to LabVIEW. The angle sensor is installed at the joint of the hydraulic robotic arm, and the pressure sensor is built into the control valve.

[0089] In a specific implementation, the proposed controller was tested on a hydraulic robotic arm. The robotic arm consists of a lateral joint, upper arm joint, lower arm joint, wrist joint, and a gripper on the end effector. A proportional valve precisely regulates the output flow. Joint angles are measured using a high-precision angle sensor operating in PWM output mode. Pressure data is acquired using a high-precision pressure sensor with a resolution of 1.5 Pa and a response time of less than 1 ms. The total weight of the robotic arm is only 30 kg. The hydraulic system is equipped with a pump-driven motor with a rated power of 4 kW and a maximum output flow rate of 12 L / min. The sampling frequency of the entire program is 500 Hz. Four parameter estimation algorithms were compared under a fixed 10 kg load condition.

[0090] Finite-time convergence method: The controller proposed in this invention ensures that the parameter estimation error converges to zero within a finite time. The adaptive parameters are set as follows: , , , .

[0091] Gradient descent: This algorithm is usually driven by tracking error and focuses only on the tracking performance of the system, rather than the convergence of specific parameters.

[0092] Recursive least squares: The algorithm uses parameter estimation error information, which allows for dynamic and iterative adjustment of the gain, providing a more flexible and adaptive approach compared to gradient descent.

[0093] Improved Adaptive Parameter Estimation: The method employs a more robust adaptive law driven by parameter estimation errors. The method optimizes the gain adaptation process, utilizing filtered error information to update parameter estimates more effectively. Gain updates also follow the rules mentioned earlier, ensuring dynamic adaptation based on error feedback.

[0094] like Figure 3 As shown, the estimation results of various parameter estimation algorithms under constant load are presented. Gradient descent failed to converge to the true value within 20 seconds. Although recursive least squares converged to the true value, driven by estimation error rather than tracking error, it exhibited significant oscillations after stabilization. The improved adaptive parameter estimation method is an extension of recursive least squares, providing higher robustness and better noise adaptation by introducing auxiliary filter matrices and vectors. Figure 3 As shown, the improved adaptive parameter estimation method produces a smoother curve; however, the filtering introduces phase lag, resulting in a slower estimation speed. In contrast, the proposed finite-time convergence method not only achieves fast convergence but also demonstrates superior steady-state performance. Quantitative analysis shows that the estimated values ​​converge to a high accuracy range of 9.75 kg to 10.14 kg between 6 s and 20 s, validating its robustness and accuracy.

[0095] Further experiments were conducted using the finite-time convergence method under different loads (7.5 kg, 10 kg, 12.5 kg, and 15 kg). Figure 4 of (a) Figure 4 (b) Figure 4 (c) and Figure 4 As shown in (d), the results confirm the algorithm's ability to accurately estimate different loads. After a brief transient phase, the estimates for all test loads converge to their true quality within 15 seconds, exhibiting only a small steady-state deviation. These results further demonstrate the robustness and effectiveness of the proposed finite-time convergence method under different load conditions.

[0096] To verify the control performance, two types of joint trajectories were designed: sinusoidal trajectory. The amplitude ,frequency , first phase Offset The trajectory is determined by the limits of each joint; and includes point-to-point trajectories, encompassing various motion states such as static, constant velocity, and constant acceleration. Taking joint 2 as an example, the corresponding reference trajectory is as follows: Figure 5 (a) and Figure 5As shown in (b), five control strategies were implemented and compared in the experiment: traditional proportional-integral-derivative control, sliding mode control, robust control, adaptive robust control, and the proposed finite-time convergent adaptive robust control. For a fair comparison, all controllers were configured with the same control parameters and operated at the same sampling frequency. The parameter settings and implementation details of each control algorithm are summarized below: C-1: The controller proposed in this invention. Parameter settings are as follows: , , , , .

[0097] C-2: Adaptive robust control, corresponding to C-1 but without a fast dynamic compensation term (i.e., ... , By setting fast compensation gain. and accomplish.

[0098] C-3: Robust control without adaptation, designed to ensure stable trajectory tracking under model uncertainty and external disturbances, without using parameter adaptation. , , Control gain () , , (Keep it the same as C-1)

[0099] C-4: Sliding mode control. The control law is designed as follows: and ,in Among them, linear feedback gain Switching gain .

[0100] C-5: A traditional proportional-integral-derivative (PID) controller, used as a benchmark. In LabVIEW, the PID control module uses an incremental design, with specific parameter settings as follows: , , .

[0101] like Figure 6 and Figure 7 As shown, the trajectory tracking performance of different control methods is illustrated under two reference trajectories: point-to-point trajectory and sinusoidal trajectory. All experiments were conducted under no-load conditions to highlight the inherent control performance of each method.

[0102] To quantitatively evaluate tracking performance, four statistical metrics were used: maximum tracking error, average tracking error, integral of absolute error, and root mean square of tracking error. Detailed quantitative results for the sinusoidal trajectory are listed in Table 1, while the results for the point-to-point trajectory are summarized in Table 2.

[0103] Table 1: Controller performance under sinusoidal trajectory

[0104] Table 2: Controller performance under point-to-point trajectories

[0105] Based on the statistical results presented in Tables 1 and 2, the proposed C-1 controller exhibits the best overall control performance, achieving minimal tracking error across all joints and trajectories. As shown in Table 1, for joint 1 on a sinusoidal trajectory, the proposed C-1 controller reduces the root mean square error by 50.9% compared to the C-2 controller. The performance improvement is even more significant compared to the baseline C-5 controller, with C-1 reducing the absolute value of the integral error by 89.4%. This trend of significant improvement applies to all joints. As shown in Table 2, C-1 maintains its robust advantage on more aggressive point-to-point trajectories. It reduces the absolute value of the integral error for joint 2 by 29.5% compared to C-2 and demonstrates excellent peak error suppression capability, with the maximum error for joint 3 being 14.8% lower than C-2 and over 61.8% lower than C-4. Joint 2 exhibits slightly larger deviations across all methods, which may be attributed to its longer link length making it more susceptible to external disturbances. Nevertheless, the overall trend remains consistent: C-1 exhibits significantly lower errors at all joints than all other control methods, confirming its consistent control accuracy and superior dynamic response.

[0106] from Figure 6 and Figure 7 The joint error curves shown indicate that C-5 exhibits significant tracking errors, particularly under complex trajectories such as point-to-point. C-4 shows some improvement in tracking performance; however, its overall accuracy remains limited, indicating that model-based methods are insufficient to effectively handle the nonlinear dynamics of hydraulic systems. C-3 maintains stable trajectory tracking even with model uncertainties, but its error level remains relatively high. C-2 significantly enhances tracking performance and reduces steady-state error through online parameter adaptive dynamic adjustment of the feedforward model compensation. In contrast, the proposed C-1 controller demonstrates the smallest tracking error under all trajectory conditions. Benefiting from the dynamic adjustment of its fast dynamic compensation term, C-1 maintains high accuracy and stability under different motion states.

[0107] In addition, such as Figure 8As shown, load experiments further validated the robustness of the proposed method. When a 10 kg load (approximately 1 / 3 of the total weight of the robotic arm) was applied to the end effector, the tracking error curves of the three joints under loaded and unloaded conditions almost overlapped. Since joint 2 is the joint most affected by load changes, it was used as a representative example, and its error curves under both operating conditions almost completely overlapped. This result demonstrates that the proposed controller is insensitive to load changes and can effectively compensate for load-induced disturbances and multi-joint dynamic coupling effects. It maintains consistent tracking performance and dynamic characteristics under constantly changing operating conditions, fully illustrating the strong robustness and practical feasibility of the proposed control method.

[0108] In summary, the controller proposed in this patent significantly enhances the control performance and adaptability of hydraulic manipulators. By reconstructing system dynamics using the generalized momentum method, an acceleration-independent regressor is developed to decouple load-related dynamics and reduce sensitivity to acceleration measurement noise. An introduced auxiliary matrix structure explicitly extracts parameter estimation error information and embeds it into a finite-time adaptive law, achieving fast and accurate estimation under various loads. Combined with a two-layer controller based on backstepping (fast direct compensation and robust feedback), asymptotic tracking convergence and strong robustness to unmodeled dynamics are achieved. Experimental results show that, compared to proportional-integral-derivative control, sliding mode control, and traditional adaptive robust controllers, the proposed method maintains stable performance even under loads reaching one-third of the manipulator's mass and affected by sensor noise. Furthermore, for nonlinear hydraulic manipulators with uncertainties and unknown loads, the framework proposed in this patent theoretically guarantees finite-time convergence of load estimation and asymptotic tracking performance of the entire controller. Future work will further expand this framework to address rapidly changing loads and multi-touch operation scenarios, enabling long-term, high-precision operations in complex and unstructured environments.

[0109] 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. A finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load, characterized in that, include: The first step is to reconstruct the system dynamics model of the multi-degree-of-freedom hydraulic manipulator using the generalized momentum method. Based on the reconstructed system dynamics model, a finite-time convergent adaptive law and a nonlinear controller based on the backstepping method are designed. The second step is to input the state information of the multi-degree-of-freedom hydraulic manipulator into the finite-time convergence adaptive law in real time, and then output the corrected adaptive gain update law after processing. The third step involves updating the adaptive gain in the nonlinear controller in real time based on the modified adaptive gain update law. At the same time, the desired trajectory and desired output thrust of the multi-degree-of-freedom hydraulic manipulator are input into the nonlinear controller. After processing, the virtual control flow is output. After nonlinear flow mapping, the valve port control voltage is obtained, and then the proportional control valve of the multi-degree-of-freedom hydraulic manipulator is controlled.

2. The finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load as described in claim 1, characterized in that: In the first step, the reconstructed system dynamics model is as follows: in, and These are the system dynamics model and its differential of a multi-degree-of-freedom hydraulic manipulator reconstructed using the generalized momentum method; and These are the momentum term and load momentum coefficient matrix of the multi-degree-of-freedom hydraulic manipulator, respectively. and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; For an unknown load on a multi-degree-of-freedom hydraulic robotic arm; and These are the inertia matrix and the coefficient matrix of the inertia matrix components of the multi-degree-of-freedom hydraulic manipulator, respectively. and These are the known dynamics and estimated friction terms and dynamics terms of a multi-degree-of-freedom hydraulic manipulator, respectively. Friction parameter vector of the robotic arm The estimated value; For unknown disturbances in a multi-degree-of-freedom hydraulic robotic arm; t For time; For non-singular joint Jacobian matrices; To output thrust for the hydraulic cylinder; and These are the gravity term and gravity term coefficient vector of the multi-degree-of-freedom hydraulic manipulator, respectively; This is the transpose of the matrix; and These are the Coriolis matrix and the coefficient matrix of the Coriolis matrix components for a multi-degree-of-freedom hydraulic manipulator, respectively. This is the regression matrix; It is a first-order low-pass filter. To pass the material through a first-order filter, a low-pass filter is first applied, and then the time derivative is taken. This represents the uncertainty and disturbance terms after filtering.

3. The finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load as described in claim 1, characterized in that: In the first step described above, the finite-time convergent adaptive law is as follows: in, and These are the adaptive gain and the corrected adaptive gain update law, respectively. Forgetting factor is a normal number; This is the adaptive gain scaling factor; This is the gain attenuation coefficient; It is an n-dimensional identity matrix; and These are the auxiliary matrix and the auxiliary vector, respectively. t 0 represents the initial time. For generalized joint torque; This is the filtered load regression matrix; This is the transpose of the matrix; and These are the joint positions and velocities of a multi-degree-of-freedom hydraulic robotic arm; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error, Update the load quality estimation law; For error integral variables; It is the Euclidean norm; The filtered uncertainty and disturbance terms; This is the positive gain adjustment parameter; The status information of a multi-degree-of-freedom hydraulic robotic arm includes the joint positions of the multi-degree-of-freedom hydraulic robotic arm. and speed The pressure in the rodless chamber of the hydraulic cylinder of a multi-degree-of-freedom hydraulic robotic arm. Pressure in the rod chamber The area of ​​the rodless and rod chambers of the hydraulic cylinder and .

4. The finite-time convergence adaptive robust control method for a hydraulic robotic arm under unknown load as described in claim 2, characterized in that: In the first step, the nonlinear controller is specifically as follows: in, , and These are respectively the virtual control flow and its adaptive feedforward and robust feedback components. For the first adaptive feedforward term, For the first fast dynamic compensation term for unmodeled dynamics and disturbances, For the first linear feedback term, This is the first nonlinear robust feedback term; This is the area-to-volume ratio coefficient of the hydraulic cylinder; For flow regression vector; For flow parameter vector The estimate; This represents the analytical part of the desired thrust derivative; The positive definite symmetric matrix for the feedback gain of the hydraulic layer. The nonlinear feedback gain of the hydraulic layer is a positive definite symmetric matrix. For thrust tracking error; and These are the adaptive robust terms and their update law, respectively. The effective bulk modulus; The estimation error of the flow parameter vector; and These are the desired output thrust and its derivative, respectively. and These are the friction parameter vectors of a multi-degree-of-freedom hydraulic robotic arm. The estimated value and its derivative; This is an estimate of the acceleration of a multi-degree-of-freedom hydraulic manipulator; for t Momentary flow uncertainty and disturbances; This is the first preset limit; The second positive definite symmetric adaptive gain coefficient; This represents the upper limit of hydraulic disturbance. For hydraulic disturbance parameters, for t Momentary flow uncertainty and disturbance The upper bound of uncertainty; For position tracking error, For speed tracking error; For the desired trajectory; and These are the virtual control quantity and its derivative; It is a positive definite feedback gain matrix; For non-singular joint Jacobian matrices; For the desired thrust adaptive feedforward compensation part, This is the second adaptive feedforward. For the second fast dynamic compensation term for unmodeled dynamics and disturbances, For the desired thrust robust feedback part, This is the second linear feedback part. This is the second nonlinear robust feedback term; This is the load dynamics regression matrix; and Unknown loads of multi-degree-of-freedom hydraulic robotic arms The estimated value and the estimation error; The second derivative of the virtual control quantity; For the linear part of the feedback gain matrix, It is a positive definite matrix for nonlinear robust feedback; and These are the estimates of the uncertainty in modeling at the joint level and their derivatives, respectively. This is the second preset limit; The first positive definite symmetric adaptive gain parameter; This is the upper bound for the uncertainty of unknown perturbations. For unknown disturbance parameters; and These are the areas of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and These are the volumes of the rodless chamber and the rod chamber of the hydraulic cylinder, respectively. and They are respectively t The definitive nominal values ​​of the flow rates in the rodless and rod chambers of the hydraulic cylinder at all times.

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