An Active Disturbance Rejection Backstepping Control System for a Wrist Rehabilitation Robot

Abstract

The present invention relates to the technical field of rehabilitation robot control, and particularly to an active disturbance rejection backstepping control system for a wrist rehabilitation robot. The wrist rehabilitation robot uses two pneumatic artificial muscle systems as driving elements. The control system includes: a tracking differentiator for tracking and differentiating the input target angle signal; an extended state observer for estimating the system state and the total system disturbance in real time; a non-linear error feedback controller for forming an error feedback signal and generating a control torque; a backstepping controller for calculating and distributing the output pressure of the pneumatic artificial muscle system; a PID controller for dynamically correcting the output pressure; and an adaptive combination valve for controlling the pressure within the pneumatic artificial muscle system. The present invention overcomes the problems of the inherent high non-linearity, uncertainty, and hysteresis effect of the pneumatic artificial muscle system, and realizes high-precision trajectory tracking control of wrist joint movement.

Description

Technical Field

[0001] The present invention relates to the technical field of rehabilitation robot control, and particularly relates to an active disturbance rejection backstepping control system for a wrist rehabilitation robot. Background Art

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

[0003] To address this problem, the solution of robot-assisted rehabilitation has gradually attracted the attention of researchers. Robots can provide high-precision and repetitive training for patients with minimal supervision, thus reducing the workload of rehabilitation therapists and improving the efficiency and effectiveness of rehabilitation training at the same time. In the past few decades, researchers have developed a variety of wrist joint rehabilitation robot devices. These devices include single-degree-of-freedom and multi-degree-of-freedom wrist rehabilitation robots, which can perform various 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 the rigid exoskeleton structure. Their advantages are high control precision, strong stiffness, and accurate motion trajectory. However, due to the strong rigidity of the rigid structure, when the movement exceeds the maximum bearing angle of the patient, it may cause secondary damage to the wrist joint, limiting its application in flexible rehabilitation.

[0004] To improve the flexibility of the rehabilitation device, 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-mass ratio, and compact structure, and are more suitable for the rehabilitation training needs of the human body. However, pneumatic artificial muscles have significant hysteresis, creep effects, and complex friction problems in actual applications, making the robot system driven by them exhibit high nonlinearity, uncertainty, and time-variation. These factors are coupled with each other, resulting in complex dynamic characteristics of the pneumatic system. Traditional linear control methods (such as PID control) are difficult to effectively address these complex nonlinear and uncertainty problems and cannot achieve precise trajectory tracking control of wrist joint movement. Summary of the Invention

[0005] In view of this, the present invention proposes an active disturbance rejection backstepping control system for a wrist rehabilitation robot. By combining the advantages of active disturbance rejection control and backstepping control, a control strategy capable of effectively estimating and compensating for the total system disturbance is designed. This system aims to overcome problems such as the highly nonlinear and uncertain nonlinear characteristics of the pneumatic artificial muscle system and achieve high-precision trajectory tracking control for the wrist rehabilitation robot.

[0006] The technical solution of the present invention is implemented as follows: The present invention provides an active disturbance rejection backstepping control system for a wrist rehabilitation robot. The wrist rehabilitation robot uses two pneumatic artificial muscle systems as driving elements, labeled as pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2. Pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 form a pneumatic artificial muscle system module. The control system includes:

[0007] A tracking differentiator for tracking and differentiating the input target angle signal to generate a tracking signal and a differential signal;

[0008] An extended state observer for real-time estimating the system state and the total system disturbance and outputting a state estimation value;

[0009] A nonlinear error feedback controller for forming an error feedback signal based on the tracking signal, the differential signal, and the state estimation value and generating a control torque;

[0010] A backstepping controller for calculating and distributing the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 based on the control torque using the dynamic model of the single-joint robotic arm;

[0011] A PID controller for dynamically correcting the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 to compensate for the hysteresis effect of the proportional pressure valve;

[0012] An adaptive combination valve, including two proportional pressure valves, a control unit, and a pressure sensor, for executing control commands and monitoring the pressure within the pneumatic artificial muscle system module.

[0013] Based on the above technical solution, preferably, the dynamic model of the single-joint robotic arm is:

[0014] ,

[0015] where, is the control torque, J is the moment of inertia of the joint runner, which can be obtained by J = 1 / 2mr 2 ; is the joint damping coefficient; f 1 is the unknown external disturbance; is the angle turned by the joint runner; is the chamber pressure of pneumatic artificial muscle system 1, is the chamber pressure of the pneumatic artificial muscle system 2; r is the radius of the joint runner; is the output pulling force of the pneumatic artificial muscle system 1, is the output pulling force of the pneumatic artificial muscle system 2; is the shrinkage 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;

[0016] Take b0 = 1 / J, and regard as the total system disturbance , let , then the state - space expression of the system can be obtained as:

[0017] ,

[0018] In the formula, f s is the total system disturbance, including unknown external disturbances.

[0019] On the basis of the above technical solution, preferably, the tracking differentiator is designed as follows:

[0020] ,

[0021] In the formula, The specific expression is as follows:

[0022]

[0023] Among them:

[0024]

[0025] In the formula: is the speed factor of the tracking differentiator, The larger it is, the faster the tracking speed; is the filtering factor of the differential tracker; is the input target angle signal of the tracking differentiator; is the input tracking signal of the tracking differentiator; is 's differential signal.

[0026] On the basis of the above technical solution, preferably, regard the unknown non - linear term of the control system as the state variable of the extended state observer, and let 's derivative be , that is , and design a third - order extended state observer as follows:

[0027]

[0028] Wherein, is the angle observation value and the error from the output angle . , and are respectively , and 's estimated values, , and are respectively the gain coefficients of the extended state observer; The function is defined as follows:

[0029]

[0030] Wherein, , i = 1, 2, 3; is the linear interval length, is the feedback power.

[0031] Based on the above technical solution, preferably, the non-linear error feedback controller is designed as follows:

[0032]

[0033] Wherein, , are the errors between the given angle , the given angular velocity and the angle estimated value , the angular velocity estimated value .

[0034] Based on the above technical solution, preferably, the implementation process of the backstepping controller includes:

[0035] A1. Based on the control torque, using the inverse operation of the dynamic model of the single-joint robotic arm, calculate the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 when the wrist joint system of the pneumatic artificial muscle system module rotates angle.

[0036] 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.

[0037] Based on the above technical solution, preferably, the calculation expression of the mathematical model of the pneumatic artificial muscle system is as follows:

[0038]

[0039] Wherein, is the output pulling force of the pneumatic artificial muscle system module, is the contraction rate of the pneumatic artificial muscle system module, is the chamber pressure of the pneumatic artificial muscle system module.

[0040] Based on the above technical solutions, preferably, the calculation expressions for the output pulling force of the pneumatic artificial muscle system 1 and the output pulling force of the pneumatic artificial muscle system 2 are as follows:

[0041]

[0042] Wherein, is the output pulling force of the pneumatic artificial muscle system 1, is the output pulling force of the pneumatic artificial muscle system 2, is the control torque;

[0043] The calculation expressions for the output pressure of the pneumatic artificial muscle system 1 and the output pressure of the pneumatic artificial muscle system 2 are as follows:

[0044]

[0045] Wherein, is the output pressure of the pneumatic artificial muscle system 1; is the output pressure of the pneumatic artificial muscle system 2.

[0046] Based on the above technical solutions, preferably, the control system further includes: a sine wave function generation module for generating a target angle signal:

[0047]

[0048] Wherein, 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;

[0049] A minimum acceleration model generation module for generating an optimal motion curve of the wrist:

[0050]

[0051] Wherein, is the initial position of the joint movement, is the stop position of the joint movement, is the period of the optimal control curve of the wrist movement, is the number of repetitions of the wrist movement control curve, is the time value, is the interval time, is the moment when the joint movement stops, is the moment when the joint movement starts.

[0052] Based on the above technical solutions, preferably, the operation process of the control system is as follows:

[0053] S1. The tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal;

[0054] S2. The extended state observer estimates the system state and the total disturbance according to the system input and output;

[0055] S3. The nonlinear error feedback controller generates the required control torque of the system based on the state estimation and the disturbance estimation;

[0056] S4. The backstepping controller distributes the required output pressures of 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;

[0057] S5. The PID controller performs tracking control on the output pressures of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2;

[0058] S6. The adaptive combination valve executes the control instruction to adjust the gas pressure in the pneumatic artificial muscle system module;

[0059] 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.

[0060] The active disturbance rejection backstepping control system of the wrist rehabilitation robot of the present invention has the following beneficial effects compared with the prior art:

[0061] (1) The present invention proposes a control system for a wrist rehabilitation robot that combines the active disturbance rejection control and the backstepping control strategy. Using the pneumatic artificial muscle system as the driving element, through the collaborative work of modules such as the tracking differentiator, the extended state observer, the nonlinear error feedback controller, the backstepping controller, and the PID controller, the system can achieve high-precision trajectory tracking control of the wrist joint movement, while providing the adaptability of flexible drive and the safety of rehabilitation training; improving the efficiency and effect of wrist joint rehabilitation training, and providing reliable technical support for the field of wrist rehabilitation robots;

[0062] (2) A tracking differentiator is used to smooth the input target angle signal, generating 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 a high-quality input signal for the subsequent controller, avoiding control instability caused by signal fluctuations, thereby ensuring the stability and accuracy of the system;

[0063] (3) An extended state observer is used to estimate the system state and total disturbance in real time, providing accurate state information and disturbance compensation ability for the control system. The core lies in treating the unknown disturbance as an extended state and observing it in real time, effectively solving the uncertainty problems caused by external disturbances and internal nonlinearities in the pneumatic artificial muscle system, and improving the anti-interference ability and control accuracy of the system;

[0064] (4) Through the nonlinear error feedback mechanism, it can quickly respond to changes in the input signal, suppress error accumulation, and ensure high-precision control of the system in complex environments, meeting the high requirements for trajectory tracking in wrist joint rehabilitation training;

[0065] (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 pressures of the pneumatic artificial muscle systems 1 and 2 are accurately calculated. By reasonably distributing the driving force, the smoothness and accuracy of the wrist joint movement are ensured, and at the same time, the dynamic response ability of the system is improved;

[0066] (6) The output pressure of the pneumatic artificial muscle system module is dynamically corrected by the PID controller, compensating for the hysteresis effect of the proportional pressure valve, adjusting the pressure control parameters in real time, improving the accuracy and robustness of the pressure control, and ensuring the stability of the drive system during the rehabilitation training process;

[0067] (7) The gas pressure in the pneumatic artificial muscle system module is monitored and adjusted in real time by the adaptive combination valve, ensuring the flexible drive characteristics of the pneumatic artificial muscle system and meeting the requirements for safety and adaptability in the rehabilitation training. Description of the Drawings

[0068] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0069] Figure 1 It is the system structure diagram of the wrist rehabilitation robot of the present invention;

[0070] Figure 2The wrist joint device diagram and the device structure schematic diagram of the pneumatic artificial muscle of the present invention;

[0071] Figure 3 The structure diagram of the active disturbance rejection backstepping control system of the present invention;

[0072] Figure 4 The experimental result diagram of the torque generated by the active disturbance rejection control algorithm for sinusoidal trajectory tracking control of the present invention;

[0073] Figure 5 The experimental result diagram of the PAM1 pressure distribution by the backstepping method for sinusoidal trajectory tracking control of the present invention;

[0074] Figure 6 The experimental result diagram of the PAM2 pressure distribution by the backstepping method for sinusoidal trajectory tracking control of the present invention;

[0075] Figure 7 The experimental result diagram of the ADRBSC sinusoidal trajectory tracking control of the present invention;

[0076] Figure 8 The experimental result diagram of the torque generated by the active disturbance rejection control algorithm for the optimal curve trajectory control of the wrist of the present invention;

[0077] Figure 9 The experimental result diagram of the PAM1 pressure distribution by the backstepping method for the optimal curve trajectory tracking control of the wrist of the present invention;

[0078] Figure 10 The experimental result diagram of the PAM2 pressure distribution by the backstepping method for the optimal curve trajectory tracking control of the wrist of the present invention;

[0079] Figure 11 The experimental result diagram of the ADRBSC optimal curve trajectory tracking control of the wrist of the present invention. Specific embodiments

[0080] Next, in combination with the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0081] As Figure 1 shown, the present invention provides an active disturbance rejection backstepping control system for a wrist rehabilitation robot. The wrist rehabilitation robot uses 2 pneumatic artificial muscle systems as driving elements, labeled 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 form a pneumatic artificial muscle system module. The control system includes:

[0082] A tracking differentiator for tracking and differentiating an input target angle signal to generate a tracking signal and a differential signal;

[0083] An extended state observer for real-time estimating the system state and the total system disturbance and outputting a state estimation value;

[0084] A non-linear error feedback controller for forming an error feedback signal based on the tracking signal, the differential signal and the state estimation value and generating a control torque;

[0085] 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 by using the dynamic model of the single-joint robotic arm;

[0086] A PID controller for tracking control of the output pressures of the pneumatic artificial muscle system 1 and the pneumatic artificial muscle system 2;

[0087] An adaptive combination valve, including two proportional pressure valves, a control unit and a pressure sensor, for executing control instructions and monitoring the pressure within the pneumatic artificial muscle system module.

[0088] Specifically, the active disturbance rejection backstepping control system of the wrist rehabilitation robot provided by the present invention overcomes the highly non-linear and uncertain problems of the pneumatic artificial muscle system (PAM) by combining the advantages of active 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 the total disturbance in real time, a non-linear error feedback controller to generate an accurate control torque, a backstepping controller to reasonably distribute the output pressures 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 nature of the pressure regulation, thereby realizing the efficiency, stability and safety of flexible drive, significantly improving the rehabilitation training effect and the adaptability of the system.

[0089] Specifically, the wrist rehabilitation robot of the present invention drives a person's wrist to perform palmar flexion / dorsiflexion movements for rehabilitation operations by controlling one degree of freedom of a joint through two antagonistic PAMs. As Figure 2As shown in Fig. (a), the wrist rehabilitation robot of the present invention uses two PAMs as driving elements. The robot body mainly consists of a base, a wrist joint support frame, a rotating shaft, PAMs, displacement sensors, tension sensors, and an adaptive combination valve, etc. Among them, the base provides stable support for the entire device and fixes the wrist joint support frame and other components; the wrist joint support frame is used to fix the patient's wrist, providing support and restraint to ensure the stability of the wrist during rehabilitation training; the rotating shaft serves as the movement center of the wrist joint, connecting the PAMs and the wrist joint support frame, and converting the tension of the PAMs into the rotational movement of the wrist joint; the PAMs, as driving elements, generate tension through inflation and deflation to drive the wrist joint to achieve palmar flexion and dorsal flexion movements; the displacement sensor is connected to the rotating shaft to real-time detect the rotation angle and displacement change of the wrist joint, providing feedback data on the motion state; the tension sensor is installed at the connection between the pneumatic muscle and the rotating shaft, used to detect the tension generated by the pneumatic artificial muscle, monitor the force condition during the movement of the wrist joint, 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 inlet of the proportional pressure valve 1 is connected to the air compressor, and the outlet is connected to the pneumatic artificial muscle, used to inflate the pneumatic muscle; the inlet of the proportional pressure valve 2 is connected to the pneumatic artificial muscle, and the outlet is communicated with the atmosphere, used to release the gas inside the pneumatic muscle; the pressure sensor real-time monitors the internal pressure of the pneumatic artificial muscle 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 inflation and deflation flow rate of the pneumatic muscle.

[0090] In the case of no load and the pneumatic artificial muscle not inflated, the wrist joint is in the neutral position, and the length of the pneumatic muscle is the initial length. When palmar flexion or dorsal flexion movement is required, the control system inflates one side of the PAM (such as PAM1), increasing its internal pressure, causing it to contract and generate tension; at the same time, the other side of the PAM (such as PAM2) deflates, extending its length. The tension of the PAM acts on the wrist joint support frame through the rotating shaft, driving the wrist joint to move around the rotating shaft, and the displacement sensor and tension sensor can respectively real-time monitor the displacement and tension magnitude.

[0091] Specifically, as Figure 2 shown in Fig. (b), PAM1 and PAM2 are installed on both sides of the wrist joint in an antagonistic manner, respectively responsible for the forward (palmar flexion) and reverse (dorsal flexion) movements of the wrist joint. When there is no load and the inflation pressure is 0, the initial length of the PAM module is Lori , under a certain load, both sides of the PAM are inflated to the pressure P0 , at this time the lengths of both sides of the pneumatic muscle are L0 , L0 is determined when installing the PAM structure. Among them, AC = BD = L0 , AE = BE = L3 , CE =r , When the rotation angle of the CD is such that at this time AC’ = L1 , L1 = L0 - L1 ; BD’ = L2 , L2 = L0 + L2 ; Wherein, L1 is the shrinkage of the PAM, L2 is the elongation of the PAM, , , , , from the cosine theorem:

[0092]

[0093] and From the geometric relationship, it can be obtained that:

[0094]

[0095] According to the cosine theorem, the true length of the left PAM1 L1 and the true length of the right PAM2 L2 , L1 and L2 The calculation expressions are as follows:

[0096]

[0097] According to Equation (3), L1 and L2 are obtained. Based on L1 and L2 the shrinkage rate of PAM1 and the shrinkage rate of PAM2 , and The calculation expressions are as follows:

[0098]

[0099] Based on L1 and L2 , from the cosine theorem, and can be obtained, and The calculation expressions are as follows:

[0100]

[0101] Specifically, PAM is a pneumatically actuated flexible actuator with unique dynamic characteristics, such as hysteresis characteristics and susceptibility to thermal factors. It is difficult to establish a dynamic model of pneumatic muscle. Therefore, the present invention designs a controller based on the existing static mathematical model of PAM. By simplifying the complex dynamic behavior, the relationship between the contraction rate, chamber pressure, and output tension of the pneumatic artificial muscle is directly described. First, the static mathematical model of PAM:

[0102]

[0103] In the formula, is the output tension of the PAM module, is the contraction rate of the pneumatic muscle, , 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, is a family of undetermined functions with respect to , where i = 1, 2, 3; , and are fitting coefficients, is 's nonlinear attenuation coefficient.

[0104] Specifically, in the static mathematical model, the output tension of PAM is decomposed into three parts. Among them, is the tension part that varies linearly with the chamber pressure, is the compensation part that varies with the chamber pressure, is the nonlinear part that varies exponentially with the contraction rate.

[0105] By linear fitting, the function is simplified. Assume ; ; , substituting the above assumptions into Equation (6), we get:

[0106]

[0107] In the formula, , representing the amplification effect of air pressure on the output tension. At different contraction rates, the response sensitivity of the output tension to air pressure is different; , representing the nonlinear force caused by the geometric and material properties of PAM itself.

[0108] Furthermore, through experimental data for k11 , k12, k21 , k22 , k31 and k32 are fitted to obtain the following calculation expression of the PAM mathematical model:

[0109]

[0110] In the formula, is the output tensile force of the PAM module, is the shrinkage rate of the PAM module, is the chamber pressure of the PAM module. It should be noted that the PAM module includes PAM1 and PAM2. This PAM mathematical model is applicable to both PAM1 and PAM2. Therefore, when calculating PAM1, the output tensile force of the PAM module is the output tensile force 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 tensile force of the PAM module is the output tensile force 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.

[0111] Specifically, the present invention further includes two proportional pressure valves. The control rate of the proportional pressure valve is approximately linearly related to the control output pressure. The expression of the proportional pressure valve model is as follows:

[0112]

[0113] In the formula, u represents the control rate of the proportional pressure valve, p represents the control output pressure of the proportional pressure valve, k1 and b1 are fitting coefficients.

[0114] Due to the influence of the friction between the valve core and the valve seat and other effects, the proportional pressure valve will exhibit a hysteresis phenomenon, resulting in a situation where the output p of the proportional valve and the input change u have a lag or asymmetry. Therefore, the coefficients k1 , b1 in Equation (9) are variable.

[0115] Specifically, through relevant mechanical and physical theories, the dynamic model of a single-joint robotic arm can be described as:

[0116]

[0117] In the formula, is the control torque, J is the moment of inertia of the joint runner, which can be obtained from J = 1 / 2mr 2 ; is the joint damping coefficient; f 1 is the unknown external disturbance; is the angle rotated by the joint runner; is the chamber pressure of PAM1, is the chamber pressure of pneumatic PAM2; r is the radius of the joint runner; is the output tension 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;

[0118] After arranging Equation (10), the following expression can be obtained:

[0119]

[0120] Take b0 = 1 / J, and regard as the total system disturbance , and rewrite Equation (11) as:

[0121]

[0122] Let , and write Equation (12) in the state - space expression:

[0123]

[0124] In the formula, f s is the total system disturbance, including the unknown external disturbance.

[0125] The active disturbance rejection backstepping control system provided by the present invention uses the combination of backstepping method and active disturbance rejection sliding - mode controller to jointly achieve the precise control of the joint angle, and its structure diagram is as shown in Figure 3 . The active disturbance rejection backstepping control system includes a tracking differentiator, an extended state observer, a non - linear error feedback controller, and a backstepping controller, and its working process is as follows:

[0126] The system receives the target angle signal v 0, and through the tracking differentiator, the signal is smoothed to generate a smooth input tracking signal v 1 and its differential signal v 2; The extended state observer estimates the system state and the total disturbance in real - time according to the input signal and output signal of the system, generates a compensation value b0n, providing accurate state information and disturbance compensation ability for subsequent control; The non - linear error feedback controller (NISEF) is based on the tracking signal v 1, differential signalv 2 and the state estimation value to generate a control torque , based on the control torque , convert it into acting forces F1 and F2 through the PAM mathematical model, and distribute them to PAM1 and PAM2 through the torque-force distribution module, and convert the acting forces F1 and F2 into pressure commands pr1 and pr2 , and send them into two PID controllers respectively 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 respectively control the forward (palmar flexion) and reverse (dorsiflexion) movements of the wrist joint. The encoder records the actual output angle of the wrist joint in real time , feedback it to the control system to form a closed-loop control to ensure that the system dynamically adjusts the control strategy according to the actual motion state

[0127] The tracking differentiator is a non-linear dynamic link for reasonably extracting 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

[0128]

[0129] In the formula The specific expression is as follows

[0130]

[0131] Among them

[0132]

[0133] In the formula is the speed factor of the tracking differentiator, The larger it is, the faster the tracking speed, which is determined by the need for the speed of the transient process and the limit ability of the system is the filtering factor of the differential tracker, The value of needs to comprehensively consider the filtering effect and the limit tracking speed of the system is the input target angle signal of the tracking differentiator is the input tracking signal of the tracking differentiator is the differential signal of

[0134] The tracking differentiator can quickly track the changes in the target angle signal by adjusting the speed factor, improving the dynamic response ability; through the optimized design of the filtering factor, it can effectively filter out high-frequency noise, generate a smooth signal, and avoid instability caused by signal fluctuations; it provides high-quality input for the extended state observer and the nonlinear error feedback controller, ensuring the accuracy of subsequent control links and achieving high-precision control of the wrist joint angle; at the same time, through reasonable parameter design, it can adapt to different target angle change requirements and enhance the robustness of the system to external disturbances and uncertainties.

[0135] The extended state observer ESO is used to estimate the state variables and the total system disturbance , the total system disturbance is continuously differentiable and bounded, and it is regarded as the extended state , The derivative of is , Actually, it is bounded, then Equation (12) is rewritten as:

[0136]

[0137] The expression of the third-order ESO is:

[0138]

[0139] In the formula, is the angle observation value and the output angle error, , and are respectively , and estimated values, , and are respectively the gain coefficients of the extended state observer; The function is defined as follows:

[0140]

[0141] Among them, , i = 1, 2, 3. is the linear interval length; is the feedback power.

[0142] The ESO uses the error between the angle observation value and the output angle, through the gain coefficient and the nonlinear function The design can quickly and accurately estimate the system state and disturbances, and feedback them to the controller for compensation. The ESO can effectively overcome the influence of unknown nonlinear terms and external disturbances in the system, significantly improve the robustness and anti-interference ability of the system; by estimating the state variables and total disturbances in real time, it provides high-precision state information for the subsequent controller to ensure the dynamic performance and stability of the control system; at the same time, the nonlinear design of the ESO enhances the adaptability to complex dynamic systems, providing important support for achieving high-precision trajectory tracking of the wrist joint.

[0143] In the present invention, to accelerate the response speed, the non-linear feedback controller adopts a non-smooth feedback method, and uses the tracking signal and the differential signal generated by the tracking differentiator TD 、 to form an error with the estimated value of the extended observer ESO and generate the initial torque

[0144]

[0145] By selecting reasonable controller parameters, so that the observed value of the state vector by the ESO can be obtained. To eliminate the influence of the total disturbance on the system, its estimated value is compensated into the control quantity, and the final torque required for the rotation

[0146]

[0147] of the pneumatic muscle wrist joint system can be obtained:

[0148] The non-linear 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 generated by it can accurately drive the pneumatic muscle wrist joint system, realizing high-precision trajectory tracking control of the wrist joint movement and improving the dynamic performance and stability of the system.

[0148] In the present invention, the execution process of the backstepping controller includes:

[0149] A1. Based on the control torque, using the inverse operation of the dynamic model of the single-joint robotic arm, calculate the output tension of PAM1 and the output tension of PAM2 when the PAM wrist joint system rotates by an angle;

[0150] 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.

[0151] Specifically, according to the backstepping principle, the control torque is generated by the active disturbance rejection control algorithm , and according to the inverse operation of the dynamic model formula (10) of the single-joint manipulator, the rotation angle of the pneumatic muscle wrist joint system, the output tension of PAM1, and the output tension of PAM2 are calculated. The specific expressions are as follows: In the formula,

[0152]

[0153] where is the output tension of PAM1, is the output tension of PAM2, is the control torque;

[0154] Substitute formula (21) into the PAM mathematical model formula (8), and after arrangement, the output pressure of PAM1 and the output pressure of PAM2 are calculated. The specific expressions are as follows:

[0155]

[0156] where is the output pressure of PAM1; is the output pressure of PAM2.

[0157] Due to the hysteresis effect of the proportional pressure valve, the relationship between the control rate u and the output pressure P is variable. According to the model-independent characteristics of the PID controller, the pressure commands required for PAM1 and PAM2 obtained by the backstepping principle can overcome these adverse factors after PID control, and the control rates of proportional valve 1 and proportional valve 2 can be corrected to obtain the final control rates u 0, u 1, so as to accurately control the pressure commands of PAM1 and PAM2, and complete the accurate trajectory tracking control of the entire system.

[0158] By combining the active disturbance rejection control algorithm and the inverse operation of the single-joint manipulator dynamic model, the backstepping controller accurately calculates the required output tension and the corresponding output pressure of the pneumatic muscle wrist joint system, and combines the model-independent characteristics of the PID controller to correct the hysteretic nonlinearity of the proportional pressure valve, ensuring the accurate control of the pressure commands of 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 joint rotation angle. Through the hierarchical recursive control of the backstepping method, the system significantly improves the trajectory tracking performance and dynamic response ability, ensuring the accuracy and robustness of the control process, and providing a reliable guarantee for the accurate and safe execution of wrist joint movements in rehabilitation training.

[0159] Specifically, the control system of the present invention further includes:

[0160] A sine wave function generation module for generating a target angle signal:

[0161]

[0162] Wherein, is the target angle signal, is the amplitude of the sine wave, is the frequency of the sine wave, is the bias of the sine wave angle.

[0163] A minimum acceleration model generation module for generating an optimal wrist motion curve. The minimum acceleration model satisfies the following mathematical law:

[0164]

[0165] In the formula, t 0 is the starting time of joint movement, θ 0 is the initial position of joint movement, t 1 is the stopping time of joint movement, θ 1 is the stopping position of joint movement, is the joint angular acceleration, which is the third derivative of the joint angle with respect to time.

[0166] Combined with the minimum acceleration model, the optimal joint angle curve is obtained through variational method:

[0167]

[0168] Maintain a certain delay time 1 / 4 at the lowest position and the highest position respectively T , and finally the optimal motion control curve law of the wrist is obtained as:

[0169]

[0170] Wherein, is the initial position of joint movement, is the stopping position of joint movement, is the period of the optimal motion control curve of the wrist, is the number of repetitions of the wrist motion control curve, is the time value, is the interval time, is the stopping time of joint movement, is the starting time of joint movement.

[0171] Specifically, in an embodiment of the present invention, the operation process of the control system is as follows:

[0172] S1. The tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differential signal;

[0173] Specifically, the tracking differentiator eliminates high-frequency noise in the input signal through a filtering algorithm (such as the gradient descent method or the sliding mode control method) to ensure that the generated signal has good continuity and differentiability.

[0174] S2. The extended state observer estimates the system state and the total disturbance based on the system input and output;

[0175] Specifically, the unknown disturbance is regarded as an extended state by using the ESO, and is estimated in real time through the observer algorithm. The introduction of the ESO significantly improves the anti-interference ability of the system, enabling the controller to maintain high-precision control in a complex non-linear environment.

[0176] S3. The non-linear error feedback controller generates the required control torque of the system based on the state estimation and the disturbance estimation;

[0177] Specifically, the non-linear 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 required control torque of the system. Its working principle is based on non-linear control theory. By designing a non-linear error feedback function, the error is non-linearly amplified or suppressed, thereby improving the dynamic performance and steady-state accuracy of the system.

[0178] S4. The backstepping controller distributes the required output pressures of PAM1 and PAM2 according to the system dynamics and the PAM mathematical model;

[0179] Specifically, the backstepping controller first calculates the output pulling force of the PAM module according to 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 non-linear control problem into multiple sub-problems to be solved one by one through a step-by-step recursive method, thereby achieving precise control of the non-linear system.

[0180] S5. The PID controller performs tracking control on the output pressures of PAM1 and PAM2;

[0181] Specifically, due to the non-linear hysteresis relationship between the output pressure of the proportional pressure valve and the control rate, the PID controller utilizes 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 the pressure control. The introduction of the PID controller significantly improves the robustness of the system, enabling it to adapt to various complex working conditions.

[0182] S6. The adaptive combination valve executes the control instruction to adjust the gas pressure in the PAM module;

[0183] 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 regulate the gas pressure within the PAM module. Specifically, the adaptive combination valve dynamically adjusts the opening degree of the proportional pressure valve by monitoring the pressure state of the PAM module in real time, thereby achieving precise control of the gas pressure.

[0184] 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.

[0185] Specifically, the encoder provides real-time position information of the wrist joint through high-precision angle measurement technology, providing crucial feedback data for the control system. The closed-loop control mechanism utilizes 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.

[0186] In an embodiment of the present invention, experiments are conducted on the active disturbance rejection backstepping control system (ADRBSC) proposed by the present invention to evaluate the performance of the ADRBSC.

[0187] The first group of experiments is sinusoidal trajectory tracking. In this experiment, the ADRBSC controller parameters are set as follows:

[0188]

[0189] The results of the first group of experiments are as Figures 4 - 7 shown. Figure 4 shows the torque generated by the active disturbance rejection control algorithm for sinusoidal trajectory tracking control. This torque is the optimal torque required for the active disturbance rejection control algorithm to allocate the wrist joint rotation required. Figure 5 shows the tracking control of the backstepping method for allocating the PAM1 pressure in sinusoidal trajectory tracking control, where the red dash line is the pressure required for the wrist joint rotation allocated by the active disturbance rejection backstepping control method for pneumatic muscle 1, and the purple solid line is the feedback pressure. Figure 6 shows the tracking control of the backstepping method for allocating the PAM2 pressure in sinusoidal trajectory tracking control, where the dark blue dash line is the pressure required for the wrist joint rotation allocated by the active disturbance rejection backstepping control method for pneumatic muscle 2, and the light blue solid line is the feedback pressure. It can be seen from the figure that for both PAM1 and PAM2 of our control algorithm, 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 shows the experimental results of the ADRBSC sinusoidal trajectory tracking control. It can be seen from the figure that the output of the tracking differentiator θr1 accurately tracks the given θd , and the rotation angle observation value is also almost the same as maintains consistency. At the beginning of the trajectory, it can be seen that the feedback trajectory can quickly track the given trajectory θ d , and can always maintain a high control accuracy in the subsequent trajectory tracking control, and the control error always remains within 2°.

[0190] The second group of experiments is the wrist optimal curve trajectory tracking. In this experiment, the ADRBSC controller parameters are set the same as those in the first group of experiments. The differences are as follows: , become 200, 40.

[0191] The results of the second group of experiments are as Figures 8 - 11 shown. Figure 8 shows the torque generated by the auto-disturbance rejection control algorithm for the wrist optimal curve trajectory control. This torque is the optimal torque required for the auto-disturbance rejection control algorithm to allocate the wrist joint rotation required. Figure 9 shows the tracking control of the backstepping method for allocating the PAM1 pressure in the wrist optimal curve trajectory tracking control, Figure 10 shows the tracking control of the backstepping method for allocating the PAM2 pressure in the wrist optimal curve trajectory tracking control. The tracking control results of the pneumatic muscle 1 and pneumatic muscle 2 pressures allocated in this way are similar to the tracking control results of the pneumatic muscle 1 and pneumatic muscle 2 pressures in the sine wave trajectory tracking control, and both can maintain a high pressure tracking control accuracy. Figure 11 shows the experimental results of the ADRBSC wrist optimal curve trajectory tracking control. Whether from the initial trajectory response speed or the overall trajectory tracking control accuracy, the wrist optimal curve trajectory is consistent with the sine wave control result and can maintain a good control effect.

[0192] The above is only the preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. An active disturbance rejection 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. Pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 form a pneumatic artificial muscle system module. The control system includes: A tracking differentiator, which is used to track and differentiate the input target angle signal to generate a tracking signal and a differentiation signal; An extended state observer, which is used to estimate the system state and the total system disturbance in real time and output the state estimation value; A non-linear error feedback controller, which is used to form an error feedback signal based on the tracking signal, the differentiation signal and the state estimation value and generate a control torque; A backstepping controller, which is used to calculate and distribute the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 based on the control torque by using the dynamic model of the single-joint manipulator; A PID controller, which is used to dynamically correct the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 to compensate for the hysteresis effect of the proportional pressure valve; An adaptive combination valve, which includes two proportional pressure valves, a control unit and a pressure sensor, and is used to execute control instructions and monitor the pressure in the pneumatic artificial muscle system module; 2. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 1, wherein The dynamic model of the single-joint robotic arm is as follows: , Wherein, is the control torque, J is the moment of inertia of the joint runner, which can be obtained by J = 1 / 2mr 2 ; is the joint damping coefficient; f 1 is the unknown external disturbance; is the angle turned by the joint runner; 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 runner; 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; taking b0 = 1 / J, and regarding as the total system disturbance , and letting , then the state space expression of the system can be obtained as:​​​ ， In the formula, f s is the total system disturbance, including unknown external disturbances.

3. The active disturbance rejection 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: Where: In the formula: is the speed factor of the tracking differentiator, the larger it is, the faster the tracking speed; is the filtering factor of the differential tracker; is the input target angle signal of the tracking differentiator; is the input tracking signal of the tracking differentiator; is the differential signal of.

4. The active disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 2, characterized in that, The unknown non - linear terms of the control system are taken as the state variables of the extended state observer. Let The derivative of be That is Design the third - order extended state observer as follows: Wherein, is the angle observation value and the output angle error, 、 and are respectively 、 and estimated values, is the extended state, 、 and are respectively the gain coefficients of the extended state observer; The function is defined as follows: Among them, , i = 1, 2, 3; is the length of the linear interval, is the feedback power.

5. The auto-disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 4, characterized in that The non-linear error feedback controller is designed as follows: In the formula, , are given angles , given angular velocities and the errors between the angle estimated values , angular velocity estimated values .

6. The active disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 1, wherein The execution process of the backstepping controller includes: A1. Based on the control torque, using the inverse operation of the dynamic model of a single-joint robotic arm, calculate the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 when calculating the rotation angle of the wrist joint system of the pneumatic artificial muscle system module. When the angle is obtained, the output tension of the pneumatic artificial muscle system 1 and the output tension of the pneumatic artificial muscle system 2 are determined. A2. Substitute the output tensile forces of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 into the mathematical model of the pneumatic artificial muscle system, and calculate the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2.

7. The active disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 6, characterized in that, The calculation expression of the mathematical model of the pneumatic artificial muscle system is as follows: Wherein, is the output pulling force of the pneumatic artificial muscle system module, is the contraction rate of the pneumatic artificial muscle system module, is the chamber pressure of the pneumatic artificial muscle system module.

8. The active disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 7, characterized in that, The calculation expressions of the output tensile forces of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 are as follows: In the formula, is the output pulling force of the pneumatic artificial muscle system 1, is the output pulling force of the pneumatic artificial muscle system 2, is the control torque, and r is the radius of the joint runner; The calculation expressions of the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 are as follows: Wherein, is the output pressure of the pneumatic artificial muscle system 1; is the output pressure of the pneumatic artificial muscle system 2.

9. The active disturbance rejection backstepping control system of a wrist rehabilitation robot according to claim 1, characterized in that, The control system further includes: a sine wave function generation module, which is used to generate a target angle signal: Among them, is the target angle signal, is the amplitude of the sine wave, is the frequency of the sine wave, is the bias of the sine wave angle; A minimum acceleration model generation module, which is used to generate the optimal motion curve of the wrist: Among them, is the initial position of joint movement, is the stop position of joint movement, is the period of the optimal control curve of wrist movement, is the number of repetitions of the wrist movement control curve, is the time value, is the interval time, is the stop moment of joint movement, is the start moment of joint movement.

10. The active 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: S1. The tracking differentiator receives the target angle signal and generates a smooth input tracking signal and its differentiation signal; S2. The extended state observer estimates the system state and the total disturbance according to the system input and output; S3. The non-linear error feedback controller generates the control torque required by the system based on the state estimation and the disturbance estimation; S4. The backstepping controller distributes the output pressures required by pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2 according to the system dynamics and the mathematical model of the pneumatic artificial muscle system; S5. The PID controller performs dynamic tracking control on the output pressures of pneumatic artificial muscle system 1 and pneumatic artificial muscle system 2; S6. The adaptive combination valve executes the control instruction and adjusts 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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