Active-disturbance-rejection backstepping control system of wrist rehabilitation robot

Abstract

The invention relates to the technical field of rehabilitation robot control, in particular to an active-disturbance-rejection backstepping control system of a wrist rehabilitation robot. The wrist rehabilitation robot adopts two pneumatic artificial muscle systems as driving elements, and the control system comprises a tracking differentiator used for tracking and differentiating an input target angle signal; the extended state observer is used for estimating the system state and the total disturbance of the system in real time; the nonlinear error feedback controller is used for forming an error feedback signal and generating a control torque; the backstepping method controller is used for calculating and distributing the output pressure of the pneumatic artificial muscle system; the PID controller is used for dynamically correcting the output pressure; and the self-adaptive combination valve is used for controlling the pressure in the pneumatic artificial muscle system. According to the method, the inherent problems of high nonlinearity, uncertainty and hysteresis effect of a pneumatic artificial muscle system are solved, and high-precision trajectory tracking control over wrist joint movement is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of rehabilitation robot control, and in particular to an anti-disturbance backstepping control system of a wrist rehabilitation robot. Background Art

[0002] Wrist dysfunction is a common movement disorder, and repeated physical training is a conventional method to restore wrist movement function. However, providing long-term, repeated physical training for a large number of people who need rehabilitation requires a large number of full-time technicians, and the lack of medical resources restricts the rehabilitation process. To address this problem, researchers have proposed a solution for robot-assisted rehabilitation, which can provide users with more precise and repetitive training with minimal supervision.

[0003] In response to this problem, robot-assisted rehabilitation solutions have gradually attracted the attention of researchers. Robots can provide patients with high-precision and repetitive training with minimal supervision, thereby reducing the workload of rehabilitation therapists and improving the efficiency and effectiveness of rehabilitation training. In the past few decades, researchers have developed a variety of wrist rehabilitation robot devices. These devices include single-degree-of-freedom and multi-degree-of-freedom wrist rehabilitation robots that can complete a variety of wrist joint movements such as palmar flexion / dorsiflexion, radial deviation / ulnar deviation, and abduction / adduction. Most rehabilitation robots are driven by motors and belong to rigid exoskeleton structures. Their advantages are high control accuracy, strong rigidity, and accurate motion trajectory. However, due to the strong rigidity of the rigid structure, when the movement exceeds the patient's maximum tolerance angle, it may cause secondary damage to the wrist joint, limiting its application in flexible rehabilitation.

[0004] In order to improve the flexibility of rehabilitation devices, some researchers have begun to use pneumatic drive devices, such as pneumatic artificial muscles. Compared with traditional motor drives, pneumatic artificial muscles have the advantages of good flexibility, high power-to-weight ratio, and compact structure, which are more suitable for human rehabilitation training needs. However, pneumatic artificial muscles have significant hysteresis, creep effect, and complex friction in practical applications, which makes the robot system driven by them show high nonlinearity, uncertainty, and time-varying properties. These factors are coupled with each other, resulting in complex dynamic characteristics of pneumatic systems. Traditional linear control methods (such as PID control) are difficult to effectively deal with these complex nonlinear and uncertainty problems, and cannot achieve accurate trajectory tracking control of wrist joint motion. Summary of the invention

[0005] In view of this, the present invention proposes an auto-disturbance rejection backstepping control system for a wrist rehabilitation robot. By combining the advantages of auto-disturbance rejection control and backstepping control, a control strategy that can effectively estimate and compensate for the total disturbance of the system is designed. The system aims to overcome the problems of high nonlinearity and uncertainty nonlinearity of the pneumatic artificial muscle system and realize high-precision trajectory tracking control of the wrist rehabilitation robot.

[0006] The technical solution of the present invention is implemented as follows: The present invention provides an anti-disturbance backstepping control system of a wrist rehabilitation robot, the wrist rehabilitation robot uses two pneumatic artificial muscle systems as driving elements, marked as pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2, the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 constitute a pneumatic artificial muscle system module, and the control system includes: A tracking differentiator, used for tracking and differentiating an input target angle signal to generate a tracking signal and a differential signal; The extended state observer is used to estimate the system state and the total disturbance of the system in real time and output the state estimation value; A nonlinear error feedback controller, for forming an error feedback signal and generating a control torque based on a tracking signal, a differential signal and a state estimation value; A backstepping controller, for calculating and distributing the output pressures of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 based on the control torque and using a dynamic model of the single-joint robotic arm; A PID controller, used for dynamically correcting the output pressure of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 to compensate for the hysteresis effect of the proportional pressure valve; The adaptive combination valve includes two proportional pressure valves, a control unit and a pressure sensor, which are used to execute control instructions and monitor the pressure in the pneumatic artificial muscle system module.

[0007] On the basis of the above technical solution, preferably, the dynamic model of the single-joint robotic arm is: , In the formula, To control the torque, J is the moment of inertia of the joint wheel, which can be expressed as J=1 / 2mr 2 get; is the joint damping coefficient; f 1 is an unknown external disturbance; is the angle of rotation of the joint wheel; is the chamber pressure of the pneumatic artificial muscle system 1, is the chamber pressure of the pneumatic artificial muscle system 2; r is the radius of the joint wheel; is the output tension of the pneumatic artificial muscle system 1, is the output tension of the pneumatic artificial muscle system 2; is the contraction rate of the pneumatic artificial muscle system module, , is the original length of the pneumatic artificial muscle system module, L is the actual length of the pneumatic artificial muscle system module; Take b 0 =1 / J, Considered as the total disturbance of the system ,make , then the state space expression of the system can be obtained as: , In the formula, f s is the total disturbance of the system, including unknown external disturbances.

[0008] Based on the above technical solution, preferably, the tracking differentiator is designed as follows: , In the formula, The specific expression is as follows: , in: , Where: To track the speed factor of the differentiator, The larger the size, the faster the tracking speed; is the filter factor of the differential tracker; The input target angle signal for the tracking differentiator; An input tracking signal for a tracking differentiator; for The differential signal of .

[0009] On the basis of the above technical solution, preferably, the unknown nonlinear term of the control system is As the state variable of the extended state observer, let The derivative of ,Right now , design the third-order extended state observer as follows: , In the formula, is the angle observation value Output Angle The error, , and They are , and The estimated value of , and are the gain coefficients of the extended state observer respectively; The function definition is as follows: , in, , i =1,2,3; is the length of the linear interval, is the feedback power.

[0010] On the basis of the above technical solution, preferably, the nonlinear error feedback controller is designed as follows: , In the formula, , For a given angle , given angular velocity With the angle estimate , angular velocity estimate of error.

[0011] On the basis of the above technical solution, preferably, the execution process of the backstepping controller includes: A1. Based on the control torque, the inverse operation of the dynamic model of the single joint mechanical example is used to calculate the rotation of the wrist joint system of the pneumatic artificial muscle system module Angle, the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2; A2. Substitute the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 into the mathematical model of the pneumatic artificial muscle system to calculate the output pressure of the pneumatic artificial muscle system 1 and the output pressure of the pneumatic artificial muscle system 2.

[0012] On the basis of the above technical solution, preferably, the calculation expression of the mathematical model of the pneumatic artificial muscle system is as follows: , In the formula, is the output tension of the pneumatic artificial muscle system module, is the contraction rate of the pneumatic artificial muscle system module, It is the chamber pressure of the pneumatic artificial muscle system module.

[0013] On the basis of the above technical solution, preferably, the calculation expressions of the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 are as follows: , In the formula, is the output tension of the pneumatic artificial muscle system 1, is the output tension of the pneumatic artificial muscle system 2, To control torque; The calculation expressions of the output pressure of the pneumatic artificial muscle system 1 and the output pressure of the pneumatic artificial muscle system 2 are as follows: , In the formula, is the output pressure of the pneumatic artificial muscle system 1; is the output pressure of the pneumatic artificial muscle system 2.

[0014] On the basis of the above technical solution, preferably, the control system further comprises: a sine wave function generation module, which is used to generate a target angle signal: , in, is the target angle signal, is the amplitude of the sine wave, is the frequency of the sine wave, is the offset of the sine wave angle; Minimum acceleration model generation module, used to generate the optimal wrist motion curve: , in, is the initial position of the joint movement, The stop position of the joint movement. is the period of the optimal control curve for wrist motion, is the number of times the wrist movement control curve is repeated, is the time value, is the interval time, The moment when the joint movement stops. This is the moment when joint movement begins.

[0015] On the basis of the above technical solution, preferably, the operation process of the control system is: S1, the tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal; S2, the extended state observer estimates the system state and total disturbance based on the system input and output; S3, a nonlinear error feedback controller generates the control torque required by the system based on state estimation and disturbance estimation; S4, the backstepping controller distributes the output pressure required by the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 according to the system dynamics and the mathematical model of the pneumatic artificial muscle system; S5, the PID controller tracks and controls the output pressure of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2; S6, the adaptive combination valve executes the control command to adjust the gas pressure in the pneumatic artificial muscle system module; S7. The encoder records the rotation angle of the wrist joint in real time and feeds it back to the control system to form a closed-loop control.

[0016] The anti-disturbance backstepping control system of the wrist rehabilitation robot of the present invention has the following beneficial effects compared with the prior art: (1) The present invention proposes a wrist rehabilitation robot control system that combines anti-disturbance control with backstepping control strategies. The system uses a pneumatic artificial muscle system as a driving element. Through the coordinated work of modules such as tracking differentiator, extended state observer, nonlinear error feedback controller, backstepping controller and PID controller, the system can achieve high-precision trajectory tracking control of wrist joint movement, while providing flexible drive adaptability and rehabilitation training safety; it improves the efficiency and effect of wrist joint rehabilitation training, and provides reliable technical support for the field of wrist rehabilitation robots; (2) The input target angle signal is smoothed by a tracking differentiator to generate a smooth tracking signal and its differential signal, eliminating high-frequency noise in the input signal and optimizing the dynamic response performance. This module provides high-quality input signals for subsequent controllers, avoiding control instability caused by signal fluctuations, thereby ensuring the stability and accuracy of the system. (3) The extended state observer estimates the system state and total disturbance in real time, providing the control system with accurate state information and disturbance compensation capability. The core of this method is to regard unknown disturbances as extended states and observe them in real time, which effectively solves the uncertainty problem caused by external disturbances and internal nonlinearity in the pneumatic artificial muscle system and improves the system's anti-interference ability and control accuracy. (4) Through the nonlinear error feedback mechanism, it can quickly respond to changes in input signals, suppress error accumulation, ensure high-precision control of the system in complex environments, and meet the high requirements of trajectory tracking for wrist joint rehabilitation training; (5) By combining the backstepping controller with the dynamic model of the single-joint robotic arm, the complex nonlinear control problem is decomposed into multiple sub-problems in a step-by-step recursive manner, and the output pressure of the pneumatic artificial muscle system 1 and system 2 is accurately calculated. By reasonably allocating the driving force, the smoothness and accuracy of the wrist joint movement are ensured, and the dynamic response capability of the system is improved. (6) The output pressure of the pneumatic artificial muscle system module is dynamically corrected through the PID controller, the hysteresis effect of the proportional pressure valve is compensated, the pressure control parameters are adjusted in real time, the accuracy and robustness of the pressure control are improved, and the stability of the drive system is ensured during the rehabilitation training process; (7) The gas pressure in the pneumatic artificial muscle system module is monitored and adjusted in real time through an adaptive combination valve, ensuring the flexible driving characteristics of the pneumatic artificial muscle system and meeting the safety and adaptability requirements of rehabilitation training. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Figure 1 is a system structure diagram of the wrist rehabilitation robot of the present invention; Figure 2 A diagram of the wrist joint device and a simplified diagram of the device structure of the pneumatic artificial muscle of the present invention; Figure 3 It is a structural diagram of the automatic disturbance rejection backstepping control system of the present invention; Figure 4 The experimental result diagram of torque generation by the sinusoidal wave trajectory tracking control self-disturbance rejection control algorithm of the present invention; Figure 5 The experimental result diagram of allocating PAM1 pressure by the backstepping method of the sine wave trajectory tracking control of the present invention; Figure 6 The experimental result diagram of allocating PAM2 pressure by the backstepping method of the sine wave trajectory tracking control of the present invention; Figure 7 Graph showing the experimental results of the ADRBSC sinusoidal wave trajectory tracking control of the present invention; Figure 8 The experimental result diagram of torque generation by the wrist optimal curve trajectory control self-disturbance rejection control algorithm of the present invention; Fig. 9 The experimental result diagram of allocating PAM1 pressure by the backstepping method of wrist optimal curve trajectory tracking control of the present invention; Fig.10 The experimental result diagram of allocating PAM2 pressure by the backstepping method of wrist optimal curve trajectory tracking control of the present invention; Fig.11 This is a diagram of the experimental results of the optimal curve trajectory tracking control of the ADRBSC wrist of the present invention. DETAILED DESCRIPTION

[0019] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] like Figure 1 As shown, the present invention provides an anti-disturbance backstepping control system of a wrist rehabilitation robot. The wrist rehabilitation robot uses two pneumatic artificial muscle systems as driving elements, marked as pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2. The pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 constitute a pneumatic artificial muscle system module. The control system includes: A tracking differentiator, used for tracking and differentiating an input target angle signal to generate a tracking signal and a differential signal; The extended state observer is used to estimate the system state and the total disturbance of the system in real time and output the state estimation value; A nonlinear error feedback controller, for forming an error feedback signal and generating a control torque based on a tracking signal, a differential signal and a state estimation value; A backstepping controller, for calculating and distributing the output pressures of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 based on the control torque and using a dynamic model of the single-joint robotic arm; A PID controller, used for tracking and controlling the output pressure of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2; The adaptive combination valve includes two proportional pressure valves, a control unit and a pressure sensor, which are used to execute control instructions and monitor the pressure in the pneumatic artificial muscle system module.

[0021] Specifically, the self-disturbance rejection backstepping control system of the wrist rehabilitation robot provided by the present invention overcomes the high nonlinearity and uncertainty problems of the pneumatic artificial muscle system (PAM) by combining the advantages of self-disturbance rejection control and backstepping control, and realizes high-precision trajectory tracking control of the wrist joint movement; the system uses a tracking differentiator to generate a smooth input signal, an extended state observer to estimate the system state and total disturbance in real time, a nonlinear error feedback controller to generate precise control torque, a backstepping controller to reasonably distribute the output pressure of the PAM module based on the dynamic model, a PID controller to dynamically correct the pressure to compensate for the hysteresis effect of the proportional pressure valve, and an adaptive combination valve to ensure the accuracy and real-time performance of the pressure regulation, thereby realizing the high efficiency, stability and safety of the flexible drive, and significantly improving the effect of rehabilitation training and the adaptability of the system.

[0022] Specifically, the wrist rehabilitation robot of the present invention controls one degree of freedom of the joint through two antagonistic PAMs to drive the human wrist to perform palmar flexion / dorsiflexion movements to perform rehabilitation work. Figure 2 As shown in (a), the wrist rehabilitation robot of the present invention uses two PAMs as driving elements, and the robot body is mainly composed of a base, a wrist support frame, a rotating shaft, a PAM, a displacement sensor, a tension sensor, and an adaptive combination valve. The base provides stable support for the entire device, fixes the wrist support frame and other components; the wrist support frame is used to fix the patient's wrist, provide support and constraint, and ensure the stability of the wrist during rehabilitation training; the rotating shaft is used as the movement center of the wrist joint, connecting the PAM and the wrist support frame, and converting the tension of the PAM into the rotational movement of the wrist joint; the PAM is used as a driving element, generating tension through inflation and deflation, and driving the wrist joint to achieve palmar flexion and dorsiflexion movement; the displacement sensor is connected to the rotating shaft, real-time detection of the rotation angle and displacement change of the wrist joint, and provides feedback data of the movement state; the tension sensor is installed at the connection between the pneumatic muscle and the rotating shaft, and is used to detect the tension generated by the pneumatic artificial muscle, monitor the force condition of the wrist joint during movement, and ensure the safety of rehabilitation training. The adaptive combination valve includes a proportional pressure valve 1, a proportional pressure valve 2 control unit and a pressure sensor. The air inlet of the proportional pressure valve 1 is connected to the air compressor, and the air outlet is connected to the pneumatic artificial muscle, which is used to inflate the pneumatic muscle; the air inlet of the proportional pressure valve 2 is connected to the pneumatic artificial muscle, and the air outlet is connected to the atmosphere, which is used to release the gas inside the pneumatic muscle; the pressure sensor monitors the internal pressure of the pneumatic artificial muscle in real time and transmits the data to the control unit; the control unit adjusts the opening of the proportional pressure valve according to the output signal of the control system to control the charging and discharging flow of the pneumatic muscle.

[0023] When there is no load and the pneumatic artificial muscle is not inflated, the wrist joint is in a neutral position and the length of the pneumatic muscle is the initial length. When palmar flexion or dorsiflexion is required, the control system inflates the PAM on one side (such as PAM1) to increase its internal pressure, causing it to contract and generate tension; at the same time, the PAM on the other side (such as PAM2) is deflated to extend its length. The tension of the PAM acts on the wrist joint support frame through the rotating axis, driving the wrist joint to move around the rotating axis. The displacement sensor and tension sensor can monitor and detect the displacement and tension in real time, respectively.

[0024] Specifically, Figure 2 As shown in (b), PAM1 and PAM2 are installed on both sides of the wrist joint in an antagonistic manner, responsible for the forward (palmar flexion) and reverse (dorsiflexion) movements of the wrist joint respectively. When there is no load and the inflation pressure is 0, the initial length of the PAM module is L ori , under a certain load, inflate the PAM on both sides to the pressure P 0, at this time the length of the pneumatic muscles on both sides is L 0 , L 0 It is determined when installing the PAM structure. Where AC=BD= L 0 ,AE=BE= L 3 , CE= r , , when CD rotates by When AC'= L 1 , L 1 = L 0 - L 1 ; BD' = L 2 , L 2 = L 0 + L 2 ; In the formula, L 1 is the shrinkage of PAM, L 2 is the elongation of PAM, , , , , according to the cosine theorem: , and From the geometric relationship, we can get: , According to the law of cosines, the true length of the left PAM1 can be calculated. L 1 And the right PAM2 real length L 2 , L 1 and L 2 The calculation expression is as follows: , According to formula (3), we can get L 1 and L 2 ,based on L1 and L 2 Calculate the shrinkage of PAM1 and PAM2 shrinkage , and The calculation expression is as follows: , based on L 1 and L 2 , we can find out from the cosine theorem and , and The calculation expression is as follows: , Specifically, PAM is a pneumatically driven flexible actuator with unique dynamic characteristics, such as hysteresis characteristics and being easily affected by thermal factors. It is difficult to establish a dynamic model of pneumatic muscles. Therefore, the present invention designs a controller based on the existing static mathematical model of PAM. By simplifying the complex dynamic behavior, it directly describes the relationship between the contraction rate, chamber pressure and output tension of pneumatic artificial muscles. First, the static mathematical model of PAM: , In the formula, is the output tension of the PAM module, is the pneumatic muscle contraction rate, , is the initial length of the PAM module, L is the actual length of the PAM module, is the chamber pressure of the PAM module, For about A family of undetermined functions, where i=1,2,3; , and is the fitting coefficient, for The nonlinear attenuation coefficient.

[0025] Specifically, the output tension of PAM is decomposed into three parts in the static mathematical model, among which: is the tensile force that varies linearly with the chamber pressure, is the compensation part that changes with the chamber pressure, is the nonlinear part that changes with the shrinkage exponent.

[0026] Through linear fitting The function is simplified, assuming ; ; , Substituting the above assumptions into equation (6), we get: , In the formula, , which indicates the amplification effect of air pressure on the output tension. Under different shrinkage rates, the response sensitivity of the output tension to air pressure is different; , represents the nonlinear force due to the geometric and material properties of the PAM itself.

[0027] Furthermore, through experimental data k 11 , k 12 , k 21 , k 22 , k 31 and k 32 After fitting, the calculation expression of the PAM mathematical model is obtained as follows: , In the formula, is the output tension of the PAM module, is the PAM module shrinkage rate, is the chamber pressure of the PAM module. It should be noted that the PAM module includes PAM1 and PAM2, and the PAM mathematical model is applicable to both PAM1 and PAM2. Therefore, when calculating PAM1, the output tension of the PAM module is the output tension of PAM1, the shrinkage rate of the PAM module is the shrinkage rate of PAM1, and the chamber pressure of the PAM module is the chamber pressure of PAM1; when calculating PAM2, the output tension of the PAM module is the output tension of PAM2, the shrinkage rate of the PAM module is the shrinkage rate of PAM2, and the chamber pressure of the PAM module is the chamber pressure of PAM2.

[0028] Specifically, the present invention also includes two proportional pressure valves, the control rate of the proportional pressure valve is approximately linearly related to the control output pressure, and the expression of the proportional pressure valve model is as follows: , In the formula, u Indicates the control rate of the proportional pressure valve, p Indicates the control output pressure of the proportional pressure valve. k 1 and b 1 is the fitting coefficient.

[0029] Due to the influence of friction between the valve core and the valve seat, the proportional pressure valve will have hysteresis, which will cause the output of the proportional valve to p Between input changes u There is a hysteresis or asymmetry, so the coefficients in equation (9) k 1 , b 1 is mutable.

[0030] Specifically, through relevant mechanical and physical theories, the dynamic model of the single-joint robotic arm can be described as: , In the formula, To control the torque, J is the moment of inertia of the joint wheel, which can be expressed as J=1 / 2mr 2 get; is the joint damping coefficient; f 1 is an unknown external disturbance; is the angle of rotation of the joint wheel; is the chamber pressure of PAM1, The chamber pressure of the pneumatic PAM2; r is the radius of the joint wheel; is the output pull of PAM1, is the output tension of PAM2; is the shrinkage rate of the PAM module, , is the initial length of the PAM module, L is the actual length of the PAM module; By rearranging formula (10), we can get the following expression: , Take b 0 =1 / J, Considered as the total disturbance of the system , rewrite equation (11) as: , make , write equation (12) into a state space expression: , In the formula, f s is the total disturbance of the system, including unknown external disturbances.

[0031] The active disturbance rejection backstepping control system provided by the present invention uses the backstepping method and the active disturbance rejection sliding mode combined controller to achieve precise control of the joint angle. Its structure diagram is shown in FIG. Figure 3As shown. The ADRC backstepping control system includes a tracking differentiator, an extended state observer, a nonlinear error feedback controller and a backstepping controller, and its working process is as follows: The system receives the target angle signal v 0 , the signal is smoothed by the tracking differentiator to generate a smooth input tracking signal v 1 and its differential signal v 2 The extended state observer estimates the system state and total disturbance in real time based on the input and output signals of the system, and generates the compensation value b 0 n, providing accurate state information and disturbance compensation capability for subsequent control; the nonlinear error feedback controller (NISEF) is based on tracking signal v 1 , differential signal v 2 and state estimation to generate control torque , based on the control torque , which is converted into the force F through the PAM mathematical model 1 and F 2 , and is distributed to PAM1 and PAM2 through the torque-force distribution module, 1 and F 2 Convert to pressure command and , respectively, are sent to two PID controllers to dynamically correct the pressure signal to compensate for the hysteresis effect of the proportional pressure valve. PAM1 and PAM2 work in an antagonistic manner to control the forward (palmar flexion) and reverse (dorsiflexion) movements of the wrist joint, respectively. The encoder records the actual output angle of the wrist joint in real time. , and feed it back to the control system to form a closed-loop control, ensuring that the system dynamically adjusts the control strategy according to the actual motion state.

[0032] The tracking differentiator is a nonlinear dynamic link that reasonably extracts the differential signal. The input signal is processed by the tracking differentiator to obtain an input tracking signal and a differential signal. The tracking differentiator is designed as follows: , In the formula, The specific expression is as follows: , in: , Where: To track the speed factor of the differentiator, The larger the value, the faster the tracking speed, which is determined by the needs of the transition process and the system's ultimate capacity; is the filter factor of the differential tracker, The value of needs to comprehensively consider the filtering effect and the system's maximum tracking speed; The input target angle signal for the tracking differentiator; An input tracking signal for a tracking differentiator; for The differential signal of .

[0033] The tracking differentiator quickly tracks the changes of the target angle signal by adjusting the speed factor to improve the dynamic response capability; through the optimization design of the filter factor, it effectively filters out high-frequency noise and generates a smooth signal to avoid instability caused by signal fluctuations; it provides high-quality input for the extended state observer and nonlinear error feedback controller to ensure the accuracy of subsequent control links and achieve high-precision control of the wrist joint angle; at the same time, through reasonable parameter design, it adapts to the needs of different target angle changes and enhances the system's robustness to external disturbances and uncertainties.

[0034] The extended state observer (ESO) is used to estimate the state variables and the total disturbance of the system. , the total disturbance of the system is continuously differentiable and bounded, and is considered an extended state , The derivative of ,Right now , In fact, it is bounded, then equation (12) can be rewritten as: , The expression of the third-order ESO is: , In the formula, is the angle observation value Output Angle The error, , and They are , and The estimated value of , and are the gain coefficients of the extended state observer respectively; The function definition is as follows: , in, , i =1,2,3. is the length of the linear interval; is the feedback power.

[0035] ESO uses the error between the angle observation value and the output angle to calculate the error through the gain coefficient and nonlinear function. The design of ESO can quickly and accurately estimate the system state and disturbance, and feed it back to the controller for compensation. ESO can effectively overcome the influence of unknown nonlinear terms and external disturbances in the system, significantly improving the robustness and anti-interference ability of the system; by estimating state variables and total disturbances in real time, it provides high-precision state information for subsequent controllers to ensure the dynamic performance and stability of the control system; at the same time, the nonlinear design of ESO enhances the adaptability to complex dynamic systems, providing important support for achieving high-precision trajectory tracking of the wrist joint.

[0036] In the present invention, in order to speed up the response speed, the nonlinear feedback controller adopts a non-smooth feedback method, using the tracking signal generated by the tracking differentiator TD and the differential signal Estimation of the extended observer ESO , Forming error and generating initial torque , the specific expression is as follows: , By choosing reasonable controller parameters, , so that the ESO state vector can be obtained Observed value , in order to eliminate the total disturbance The impact on the system is estimated Compensating to the control quantity, the rotation of the pneumatic muscle wrist joint system can be obtained Required final torque : , The nonlinear feedback controller accelerates the system response speed through non-smooth feedback design, ensuring the real-time performance of the control system; the final control torque it generates can accurately drive the pneumatic muscle wrist joint system, achieve high-precision trajectory tracking control of the wrist joint movement, and improve the dynamic performance and stability of the system.

[0037] In the present invention, the execution process of the backstepping controller includes: A1. Based on the control torque, the PAM wrist joint system rotation is calculated by using the inverse operation of the dynamic model of the single joint mechanical example. Angle, the output tension of PAM1 and the output tension of PAM2; A2. Substitute the output tension of PAM1 and the output tension of PAM2 into the PAM mathematical model to calculate the output pressure of PAM1 and the output pressure of PAM2.

[0038] Specifically, according to the backstepping principle, the control torque is generated by the active disturbance rejection control algorithm According to the inverse operation of the dynamic model of the single-joint robot (10), the rotation of the pneumatic muscle wrist joint system is solved. Angle, PAM1 output tension and PAM2 output tension, the specific expression is as follows: , In the formula, is the output pull of PAM1, is the output pull of PAM2, To control torque; Substituting equation (21) into the PAM mathematical model equation (8), after sorting, the output pressure of PAM1 and the output pressure of PAM2 are solved. The specific expressions are as follows: , In the formula, is the output pressure of PAM1; is the output pressure of PAM2.

[0039] Due to the hysteresis of the proportional pressure valve, the relationship between the control rate u and the output pressure P is variable. According to the characteristics of the PID controller that does not rely on the model, the backstepping principle is used to obtain the pressure instructions required for PAM1 and PAM2. After PID control, these unfavorable factors can be overcome, and the control rates of proportional valves 1 and 2 can be corrected to obtain the final control rate. u 0 , u 1 , thereby accurately controlling the pressure instructions of PAM1 and PAM2 and completing the precise trajectory tracking control of the entire system.

[0040] The backstepping controller combines the anti-disturbance control algorithm with the inverse operation of the single-joint robot arm dynamics model to accurately calculate the output tension and corresponding output pressure required by the pneumatic muscle wrist joint system, and combines the model-independent characteristics of the PID controller to correct the hysteresis nonlinearity of the proportional pressure valve to ensure accurate control of the pressure instructions of the pneumatic muscles PAM1 and PAM2. This design can effectively overcome the hysteresis, nonlinearity and deviation problems in PAM and achieve high-precision control of the wrist rotation angle. Through the hierarchical recursive control of the backstepping method, the system significantly improves the trajectory tracking performance and dynamic response capability, ensures the accuracy and robustness of the control process, and provides a reliable guarantee for the accurate and safe execution of wrist joint movements in rehabilitation training.

[0041] Specifically, the control system of the present invention further includes: Sine wave function generation module, used to generate target angle signal: , in, is the target angle signal, is the amplitude of the sine wave, is the frequency of the sine wave, is the offset of the sine wave angle.

[0042] The minimum acceleration model generation module is used to generate the optimal wrist motion curve. The minimum acceleration model satisfies the following mathematical rules: , In the formula, The moment when the joint movement starts. is the initial position of the joint movement, The moment when the joint movement stops. The stop position of the joint movement. is the joint angular acceleration, which is the third-order derivative of the joint angle with respect to time.

[0043] Combined with the minimum acceleration model, the optimal joint angle curve is obtained through variational conversion: , Maintain a certain delay time of 1 / 4 at the lowest position and the highest position respectively T Finally, the optimal wrist motion control curve is obtained as follows: , in, is the initial position of the joint movement, The stop position of the joint movement. is the period of the optimal control curve for wrist motion, is the number of times the wrist movement control curve is repeated, is the time value, is the interval time, The moment when the joint movement stops. This is the moment when joint movement begins.

[0044] Specifically, in one embodiment of the present invention, the operation process of the control system is: S1, the tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal; Specifically, the tracking differentiator eliminates high-frequency noise in the input signal through a filtering algorithm (such as gradient descent method or sliding mode control method) to ensure that the generated signal has good continuity and differentiability.

[0045] S2, the extended state observer estimates the system state and total disturbance based on the system input and output; Specifically, the unknown disturbance is regarded as an extended state by using ESO, and is estimated in real time by the observer algorithm. The introduction of ESO significantly improves the anti-disturbance capability of the system, enabling the controller to maintain high-precision control in complex nonlinear environments.

[0046] S3, a nonlinear error feedback controller generates the control torque required by the system based on state estimation and disturbance estimation; Specifically, the nonlinear error feedback controller generates an error feedback signal by combining the tracking signal, the differential signal and the state estimation value, and further calculates the control torque required by the system. Its working principle is based on nonlinear control theory. By designing a nonlinear error feedback function, the error is nonlinearly amplified or suppressed, thereby improving the dynamic performance and steady-state accuracy of the system.

[0047] S4, the backstepping controller allocates the required output pressures of PAM1 and PAM2 according to the system dynamics and the PAM mathematical model; Specifically, the backstepping controller first calculates the output tension of the PAM module based on the control torque, and then substitutes it into the PAM mathematical model to further solve the required output pressure. The backstepping control strategy decomposes the complex nonlinear control problem into multiple sub-problems through step-by-step recursion and solves them one by one, thereby achieving precise control of the nonlinear system.

[0048] S5, PID controller tracks and controls the output pressure of PAM1 and PAM2; Specifically, due to the nonlinear hysteresis relationship between the output pressure and the control rate of the proportional pressure valve, the PID controller uses its model-independent characteristics to dynamically compensate for the pressure error by adjusting the proportional, integral and differential parameters in real time, thereby ensuring the accuracy and real-time performance of pressure control. The introduction of the PID controller significantly improves the robustness of the system, enabling it to adapt to various complex working conditions.

[0049] S6, the adaptive combination valve executes the control instruction to adjust the gas pressure in the PAM module; Specifically, the adaptive combination valve consists of two proportional pressure valves, a control unit and a pressure sensor. Its main function is to execute control instructions and adjust the gas pressure in the PAM module. Specifically, the adaptive combination valve dynamically adjusts the opening of the proportional pressure valve by real-time monitoring of the pressure state of the gas PAM module, thereby achieving precise control of the gas pressure.

[0050] S7. The encoder records the rotation angle of the wrist joint in real time and feeds it back to the control system to form a closed-loop control.

[0051] Specifically, the encoder provides real-time position information of the wrist joint through high-precision angle measurement technology, providing key feedback data for the control system. The closed-loop control mechanism uses this feedback data to dynamically adjust the control strategy, thereby achieving high-precision control of the wrist joint movement while ensuring the stability and safety of the system.

[0052] In one embodiment of the present invention, an active disturbance rejection backstepping control system (ADRBSC) proposed in the present invention is tested to evaluate the performance of the ADRBSC.

[0053] The first set of experiments is sinusoidal wave trajectory tracking. In this experiment, the ADRBSC controller parameters are set as follows:

[0054] The results of the first set of experiments are as follows Figure 4-7 shown. Figure 4 The sinusoidal trajectory tracking control ADRC algorithm generates torque, which is the ADRC algorithm's distribution of wrist rotation. Optimum torque required. Figure 5 The figure shows the tracking control of the PAM1 pressure assigned by the sine wave trajectory tracking control backstepping method, where the red dashed line is the wrist rotation assigned by the anti-disturbance rejection backstepping control method. The pressure required by pneumatic muscle 1. The purple solid line is the feedback pressure. Figure 6 The figure shows the tracking control of the PAM2 pressure assigned by the sinusoidal trajectory tracking control backstepping method, where the dark blue dashed line is the wrist rotation assigned by the ADRC backstepping control method. The pressure required for pneumatic muscle 2, the solid blue line is the feedback pressure. It can be seen from the figure that no matter our control algorithm is for PAM1 or PAM2, the feedback pressure can quickly track the required pressure, and the control accuracy is relatively high, achieving a good pressure tracking control effect. Figure 7 The experimental results of ADRBSC sinusoidal wave trajectory tracking control are shown. From the figure, it can be seen that the output of the tracking differentiator Accurately track the given , rotation angle observation value Almost Keep it consistent. At the beginning of the trajectory, you can see the feedback trajectory Able to quickly track a given trajectory , in the subsequent trajectory tracking control, high control accuracy can always be maintained, and the control error is always kept within 2°.

[0055] The second group of experiments is the wrist optimal curve trajectory tracking. In this experiment, the ADRBSC controller parameter settings are the same as those in the first group of experiments, with the following differences: , Becomes 200, 40.

[0056] The results of the second group of experiments are as follows Figure 8-11 shown. Figure 8 The optimal wrist curve trajectory control ADRC algorithm generates torque, which is the ADRC algorithm's distribution of wrist joint rotation. Optimum torque required. Fig. 9 The tracking control of wrist optimal curve trajectory tracking control and backstepping method to distribute PAM1 pressure is shown. Fig.10 The tracking control of PAM2 pressure distribution by backstepping method of wrist optimal curve trajectory tracking control is shown. The pressure tracking control results of pneumatic muscle 1 and pneumatic muscle 2 distributed in this way are similar to those of pneumatic muscle 1 and pneumatic muscle 2 in sinusoidal wave trajectory tracking control, and both can maintain high pressure tracking control accuracy. Fig.11 The experimental results of the optimal curve trajectory tracking control of the ADRBSC wrist are shown. Whether in terms of the initial trajectory response speed or the overall trajectory tracking control accuracy, the optimal curve trajectory of the wrist is consistent with the sine wave control result, and both can maintain a good control effect.

[0057] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An anti-disturbance backstepping control system for a wrist rehabilitation robot, characterized in that: The wrist rehabilitation robot uses two pneumatic artificial muscle systems as driving elements, marked as pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2. The pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 constitute a pneumatic artificial muscle system module. The control system includes: A tracking differentiator, used for tracking and differentiating an input target angle signal to generate a tracking signal and a differential signal; The extended state observer is used to estimate the system state and the total disturbance of the system in real time and output the state estimation value; A nonlinear error feedback controller, for forming an error feedback signal and generating a control torque based on a tracking signal, a differential signal and a state estimation value; A backstepping controller, for calculating and distributing the output pressures of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 based on the control torque and using a dynamic model of the single-joint robotic arm; A PID controller, used for dynamically correcting the output pressure of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 to compensate for the hysteresis effect of the proportional pressure valve; The adaptive combination valve includes two proportional pressure valves, a control unit and a pressure sensor, and is used for executing control instructions and monitoring the pressure in the pneumatic artificial muscle system module.

2. The anti-disturbance backstepping control system of a wrist rehabilitation robot according to claim 1, characterized in that: The dynamic model of the single-joint robotic arm is: ， In the formula, To control the torque, is the moment of inertia of the joint wheel, which can be obtained by J=1 / 2mr 2 get; is the joint damping coefficient; f 1 is the unknown external disturbance; is the angle of rotation of the joint wheel; is the chamber pressure of the pneumatic artificial muscle system 1, is the chamber pressure of the pneumatic artificial muscle system 2; r is the radius of the joint wheel; is the output tension of the pneumatic artificial muscle system 1, is the output tension of the pneumatic artificial muscle system 2; is the contraction rate of the pneumatic artificial muscle system module, , is the original length of the pneumatic artificial muscle system module, L is the actual length of the pneumatic artificial muscle system module; Take b0=1 / J, and Considered as the total disturbance of the system ,make , then the state space expression of the system can be obtained as: ， In the formula, f s is the total disturbance of the system, including unknown external disturbances.

3. The anti-disturbance backstepping control system of a wrist rehabilitation robot according to claim 1, characterized in that: The tracking differentiator is designed as follows: ， In the formula, The specific expression is as follows: ， in: ， Where: To track the speed factor of the differentiator, The larger the size, the faster the tracking speed; is the filter factor of the differential tracker; The input target angle signal for the tracking differentiator; An input tracking signal for tracking differentiator; for The differential signal of .

4. The anti-disturbance backstepping control system of a wrist rehabilitation robot as claimed in claim 2, characterized in that: The unknown nonlinear terms of the control system As the state variable of the extended state observer, let The derivative of ,Right now , design the third-order extended state observer as follows: ， In the formula, is the angle observation value Output Angle The error, , and They are , and The estimated value of , and are the gain coefficients of the extended state observer respectively; The function definition is as follows: ， in, , i =1,2,3; is the length of the linear interval, is the feedback power.

5. The anti-disturbance backstepping control system of a wrist rehabilitation robot as claimed in claim 4, characterized in that: The nonlinear error feedback controller is designed as follows: ， In the formula, , For a given angle , given angular velocity With the angle estimate , angular velocity estimate of error.

6. The anti-disturbance backstepping control system of a wrist rehabilitation robot as claimed in claim 1, characterized in that: The execution process of the backstepping controller includes: A1. Based on the control torque, the inverse operation of the dynamic model of the single joint mechanical example is used to calculate the rotation of the wrist joint system of the pneumatic artificial muscle system module Angle, the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2; A2. Substitute the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 into the mathematical model of the pneumatic artificial muscle system to calculate the output pressure of the pneumatic artificial muscle system 1 and the output pressure of the pneumatic artificial muscle system 2.

7. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot as claimed in claim 6, characterized in that: The calculation expression of the mathematical model of the pneumatic artificial muscle system is as follows: ， In the formula, is the output tension of the pneumatic artificial muscle system module, is the contraction rate of the pneumatic artificial muscle system module, It is the chamber pressure of the pneumatic artificial muscle system module.

8. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot as claimed in claim 7, characterized in that: The calculation expressions of the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 are as follows: ， In the formula, is the output tension of the pneumatic artificial muscle system 1, is the output tension of the pneumatic artificial muscle system 2, To control torque; The calculation expressions of the output pressure of the pneumatic artificial muscle system 1 and the output pressure of the pneumatic artificial muscle system 2 are as follows: ， In the formula, is the output pressure of the pneumatic artificial muscle system 1; is the output pressure of the pneumatic artificial muscle system 2.

9. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot as claimed in claim 1, characterized in that: The control system further comprises: a sine wave function generating module, which is used to generate a target angle signal: ， in, is the target angle signal, is the amplitude of the sine wave, is the frequency of the sine wave, is the offset of the sine wave angle; Minimum acceleration model generation module, used to generate the optimal wrist motion curve: ， in, is the initial position of the joint movement, The stop position of the joint movement. is the period of the optimal control curve for wrist motion, is the number of times the wrist movement control curve is repeated, is the time value, is the interval time, The moment when the joint movement stops. This is the moment when joint movement begins.

10. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 1, characterized in that: The operation process of the control system is as follows: S1, the tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal; S2, the extended state observer estimates the system state and total disturbance based on the system input and output; S3, a nonlinear error feedback controller generates the control torque required by the system based on state estimation and disturbance estimation; S4, the backstepping controller distributes the output pressure required by the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2 according to the system dynamics and the mathematical model of the pneumatic artificial muscle system; S5, the PID controller dynamically tracks and controls the output pressure of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2; S6, the adaptive combination valve executes the control command to adjust the gas pressure in the pneumatic artificial muscle system module; S7. The encoder records the rotation angle of the wrist joint in real time and feeds it back to the control system to form a closed-loop control.

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