A self-disturbance rejection learning control method for a rope-driven lower limb rehabilitation exoskeleton

Abstract

A self-disturbance rejection learning control method for a rope-driven lower limb rehabilitation exoskeleton belongs to the field of exoskeleton robot control technology, and includes the following steps: 1) analyzing the relationship between the motor drive torque and the joint control torque, and establishing a dynamic model of the rope-driven lower limb rehabilitation exoskeleton; 2) designing a sliding surface to avoid the error amplification effect of the differential velocity signal; 3) designing a self-disturbance rejection learning controller and analyzing the system performance to achieve trajectory tracking control of the lower limb rope-driven rehabilitation exoskeleton. The control method of the present invention divides the uncertainty in the rope-driven exoskeleton system model into periodic uncertainty and non-periodic uncertainty, uses a linear extended state observer to estimate and compensate for periodic uncertainty, and designs a repeated learning law to estimate periodic uncertainty, thereby improving the system robustness and stability while being able to control the system tracking error at a low level. The method has a simple control law and has great application prospects for improving the control performance of the rope-driven lower limb rehabilitation exoskeleton.

Description

Technical Field

[0001] The invention belongs to the technical field of exoskeleton robot control, and in particular relates to a rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method. Background Art

[0002] As a mechatronic intelligent rehabilitation device, the lower limb exoskeleton robot can replace rehabilitation therapists to assist patients with lower limb dysfunction in repetitive and arduous rehabilitation training, and has obvious advantages in terms of repeatability, diversity, cost and efficiency. At present, most lower limb rehabilitation exoskeletons use rigid drive with the drive motor placed at the human joint. The exoskeleton body is bulky, and the motion inertia and motion burden of the affected limb are large, which limits the effect of the patient's wearable rehabilitation. In comparison, the drive of the rope-driven lower limb rehabilitation exoskeleton can be externally placed at the torso far away from the limb movement, and the Bowden rope is used to transmit power remotely, reducing the motion inertia while increasing the flexibility of the system, showing greater potential in rehabilitation applications. However, while the rope-driven lower limb rehabilitation exoskeleton increases the complexity of the mechanism, its strong nonlinear problem also increases the difficulty of system control, including the hysteresis problem caused by the inherent friction and self-flexibility of the lasso transmission, the joint friction problem, and the uncertainty interference problem caused by the coupling effect during human-machine coordinated control.

[0003] At present, for most lower limb rehabilitation exoskeleton robots, trajectory tracking control is the main control method to achieve rehabilitation training movements. For rehabilitation training based on repetitive movements, especially passive rehabilitation training, control performance plays a fundamental and even decisive role in the quality of rehabilitation. This requires not only good stability and determinism of the controller, but also good anti-disturbance performance. As can be seen from the above, the strong nonlinearity of the rope-driven lower limb rehabilitation exoskeleton makes it difficult to establish an accurate mathematical model. The model-free control method can get rid of the constraints of the system model and avoid the complex system identification and inverse kinematics calculations in the exoskeleton system. In recent years, it has been gradually applied to the field of exoskeleton control.

[0004] As a model-free control method, ADRC uses the integral standard form to construct the controlled object model to reduce the dependence on model parameters, and then uses the extended state observer to estimate and compensate for the concentrated disturbance to offset the impact of the concentrated disturbance on the system, thereby improving the robustness of the system. Therefore, ADRC is very suitable for dealing with the cooperative control problem of exoskeletons. In addition, based on the repeatability of passive rehabilitation movements and combined with the advantages of repeated learning control, it is beneficial to improve the accuracy of exoskeleton trajectory tracking control. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention provides a rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method to achieve human-machine collaborative control of the exoskeleton system, improve the system robustness and stability while controlling the system tracking error at a low level.

[0006] The technical solution of the present invention is:

[0007] A rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method comprises the following steps:

[0008] Step 1: Analyze the relationship between the motor driving torque and the joint control torque, and establish a dynamic model of the rope-driven lower limb rehabilitation exoskeleton;

[0009] Step 2: Design the sliding surface to avoid the error amplification effect of the differential velocity signal;

[0010] Step 3: Design an anti-disturbance learning controller and analyze the system performance to achieve trajectory tracking control of the lower limb rope-driven rehabilitation exoskeleton.

[0011] Optionally, the process of step 1 is as follows:

[0012] 1.1 Establishment of the double-lasso transmission system model.

[0013] (1);

[0014] In formula (1), Indicates the initial preload of the Bowden rope in the double lasso system; express The driving torque at the motor end at the moment; and Respectively The control torque at the exoskeleton joints at the moment and the previous moment; They represent the radii of the motor-end driving wheel and the exoskeleton joint driving wheel respectively; It is a sign function, which is defined as positive when the transmission is clockwise, negative when the transmission is counterclockwise, and zero when there is no transmission; is the Coulomb friction coefficient between the bushing and the Bowden cable; represents the curvature of the lasso element, is the casing length;

[0015] 1.2 Dynamic modeling of lower limb exoskeleton,

[0016] (2);

[0017] In formula (2), Respectively represent the angle, angular velocity and angular acceleration vector of each joint of the exoskeleton; is a symmetric positive definite inertia matrix, is the Coriolis force and centripetal force matrix, is the gravity matrix; Indicates the joint friction torque generated by the motor reducer and mechanism installation; represents the human-computer interaction torque;

[0018] The lower limb exoskeleton joints and the driving motors are driven by lassoes. Combining formula (1) and formula (2), the dynamic model of the rope-driven lower limb rehabilitation exoskeleton is:

[0019] (3);

[0020] In formula (3), ;

[0021] 1.3 Defining state variables , , the state space expression of the exoskeleton system is,

[0022] (4);

[0023] In formula (4), Respectively The first derivative of ; In addition, given the period is Smooth bounded trajectory of , there is an expected input satisfy,

[0024] (5);

[0025] In formula (5), is a bounded periodic signal, Respectively The first-order derivative of ; combined with equation (5), the system state space expression (4) becomes,

[0026] (6);

[0027] In formula (6), ; .

[0028] Optionally, the process of step 2 is as follows:

[0029] 2.1 Calculation of system trajectory tracking error :

[0030] (7);

[0031] 2.2 Design of sliding surface ,

[0032] (8);

[0033] In formula (8), is an adjustable parameter; yes An estimated value of yes The first derivative of ; express The observation error.

[0034] Optionally, the process of step 3 is as follows:

[0035] 3.1 Define the controller,

[0036] (9);

[0037] In formula (9), For expected input The estimated value of is the robust control term;

[0038] 3.2 Designing the Law of Repeated Learning Estimate the periodic uncertainty in system (6),

[0039] (10);

[0040] In formula (10), and Respectively exist and Estimated value of the moment; for repeated learning gains; is the limiting function, defined as,

[0041] (11);

[0042] In formula (11), express The limit value of is a symbolic function;

[0043] In addition, in formula (10) For definition in A continuous function on

[0044] (12);

[0045] 3.3 Design an extended state observer to estimate the unknown state of the system; for this purpose, rewrite equation (6) as follows:

[0046] (13);

[0047] In formula (13), ,in yes The inverse matrix of , express The estimation error of It is the known part of the system, obtained through prior knowledge; express The first derivative of is a bounded function;

[0048] For the system described by equation (13), the linear extended state observer is designed as:

[0049] (14);

[0050] In formula (14), Represent the observer state The first derivative of ; represents the bandwidth constant;

[0051] 3.4 Design of Active Disturbance Rejection Controller Compensating for non-periodic uncertainties in the system,

[0052] (15);

[0053] In formula (15), is an adjustable parameter;

[0054] Substituting equation (15) into equation (9), the ADRC is:

[0055] (16).

[0056] The technical concept of the present invention is: a strongly nonlinear rope-driven lower limb rehabilitation exoskeleton system for performing passive rehabilitation training. The uncertainty in the system is divided into periodic uncertainty and non-periodic uncertainty, and a linear extended state observer is designed to estimate the unknown state of the system and compensate for the non-periodic uncertainty of the system, thereby improving the robustness and stability of the system; at the same time, a repetitive learning law is designed to estimate the periodic uncertainty in the system, thereby improving the accuracy of the system trajectory tracking.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. The present invention overcomes the technical difficulty of accurately modeling the rope-driven lower limb rehabilitation exoskeleton system and is easy for engineering application;

[0059] 2. The present invention uses an extended state observer to estimate and compensate for the unknown state of the rope-driven lower limb rehabilitation exoskeleton system, thereby improving the robustness of the system;

[0060] 3. The present invention uses the observed speed signal instead of the differential speed signal, thus avoiding the error amplification effect of interference;

[0061] 4. The present invention is directed to exoskeleton passive rehabilitation training, and under the action of the repetitive learning law, it realizes high-precision tracking control of repetitive desired trajectories, thereby improving the effect of rehabilitation training. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 is a control system flow chart of the present invention;

[0063] Figure 2 It is the trajectory tracking diagram of the rope-driven lower limb rehabilitation exoskeleton wearable experiment based on the self-disturbance rejection control;

[0064] Figure 3 This is the trajectory error result diagram of the rope-driven lower limb rehabilitation exoskeleton wearable experiment based on the anti-disturbance control;

[0065] Figure 4 It is the trajectory tracking diagram of the rope-driven lower limb rehabilitation exoskeleton wearable experiment based on self-disturbance rejection learning control;

[0066] Figure 5 This is a trajectory error result diagram of the rope-driven lower limb rehabilitation exoskeleton wearable experiment based on self-disturbance rejection learning control;

[0067] Figure 6 It is the observation effect of the linear extended state observer based on self-disturbance rejection learning control. DETAILED DESCRIPTION

[0068] The present invention is further described below in conjunction with the accompanying drawings and embodiments, but is not intended to limit the protection scope of the present invention.

[0069] Reference Figure 1-Figure 6 , a rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method, comprising the following steps:

[0070] Step 1: Analyze the relationship between the motor driving torque and the joint control torque, and establish a dynamic model of the rope-driven lower limb rehabilitation exoskeleton. The process is as follows:

[0071] 1.1 Establishment of the double-lasso transmission system model.

[0072] (1);

[0073] In formula (1), Indicates the initial preload of the Bowden rope in the double lasso system; express The driving torque at the motor end at the moment; and Respectively The control torque at the exoskeleton joints at the moment and the previous moment; They represent the radii of the motor-end driving wheel and the exoskeleton joint driving wheel respectively; It is a sign function, which is defined as positive when the transmission is clockwise, negative when the transmission is counterclockwise, and zero when there is no transmission; is the Coulomb friction coefficient between the bushing and the Bowden cable; represents the curvature of the lasso element, is the casing length;

[0074] 1.2 Dynamic modeling of lower limb exoskeleton,

[0075] (2);

[0076] In formula (2), Respectively represent the angle, angular velocity and angular acceleration vector of each joint of the exoskeleton; is a symmetric positive definite inertia matrix, is the Coriolis force and centripetal force matrix, is the gravity matrix; Indicates the joint friction torque generated by the motor reducer and mechanism installation; represents the human-computer interaction torque;

[0077] The lower limb exoskeleton joints and the driving motors are driven by lassoes. Combining formula (1) and formula (2), the dynamic model of the rope-driven lower limb rehabilitation exoskeleton is:

[0078] (3);

[0079] In formula (3), ;

[0080] 1.3 Defining state variables , , the state space expression of the exoskeleton system is,

[0081] (4);

[0082] In formula (4), Respectively The first derivative of ; In addition, given the period is Smooth bounded trajectory of , there is an expected input satisfy,

[0083] (5);

[0084] In formula (5), is a bounded periodic signal, Respectively The first-order derivative of ; combined with equation (5), the system state space expression (4) becomes,

[0085] (6);

[0086] In formula (6), ; ;

[0087] Step 2: Design the sliding surface to avoid the error amplification effect of the differential velocity signal. The process is as follows:

[0088] 2.1 Calculation of system trajectory tracking error :

[0089] (7);

[0090] 2.2 Design of sliding surface ,

[0091] (8);

[0092] In formula (8), is an adjustable parameter; yes An estimated value of yes The first derivative of ; express In formula (8), due to the disturbance in the measurement during the actual application of the system, Alternative , to avoid the error amplification problem of the differential angular velocity signal;

[0093] Step 3: Design an anti-disturbance learning controller and analyze the system performance to achieve trajectory tracking control of the lower limb rope-driven rehabilitation exoskeleton. The process is as follows:

[0094] 3.1 Define the controller,

[0095] (9);

[0096] In formula (9), For expected input The estimated value of is the robust control term;

[0097] 3.2 Designing the Law of Repeated Learning Estimate the periodic uncertainty in system (6),

[0098] (10);

[0099] In formula (10), and Respectively exist and Estimated value of the moment; for repeated learning gains; is the limiting function, defined as,

[0100] (11);

[0101] In formula (11), express The limit value of is a symbolic function;

[0102] In addition, in formula (10) For definition in A continuous function on

[0103] (12);

[0104] 3.3 Design an extended state observer to estimate the unknown state of the system; for this purpose, rewrite equation (6) as follows:

[0105] (13);

[0106] In formula (13), ,in yes The inverse matrix of , express The estimation error of It is the known part of the system, obtained through prior knowledge; express The first derivative of is a bounded function;

[0107] For the system described by equation (13), the linear extended state observer is designed as:

[0108] (14);

[0109] In formula (14), Represent the observer state The first derivative of ; represents the bandwidth constant;

[0110] 3.4 Design of Active Disturbance Rejection Controller Compensating for non-periodic uncertainties in the system,

[0111] (15);

[0112] In formula (15), is an adjustable parameter;

[0113] Substituting equation (15) into equation (9), the ADRC is:

[0114] (16);

[0115] 3.5 Constructing Lyapunov functions , analyze system performance,

[0116] (17);

[0117] Derivative of formula (17) yields:

[0118] (18);

[0119] In formula (18), Respectively The first derivative of ; and Respectively exist and The estimated error at time , based on the inequality , And the nature ,in , Representing any real number, we have,

[0120] (19);

[0121] In formula (19), express The first derivative of ; is a normal number, satisfying , express The observation error of is a bounded parameter, ; , ;

[0122] when hour, established, so Finally converges to the interval ,at this time,

[0123] (20);

[0124] It can be seen that the system is uniformly bounded and the tracking error It eventually converges to a region near zero;

[0125] In order to verify the effectiveness of the proposed method, the control effect of the self-disturbance rejection learning controller described in formula (16) was experimentally verified. The rope-driven lower limb rehabilitation exoskeleton used in the wearable control experiment was a rope-driven knee joint exoskeleton;

[0126] Figure 1 It is a control flow chart of the present invention, which is roughly divided into two parts, namely, using an extended state observer to estimate the unknown state of the system and compensate for the non-periodic uncertainty of the system and designing a repeated learning law to estimate the periodic uncertainty in the system;

[0127] The sampling time selected in the experiment is 0.005s, and the expected trajectory of the joint is ,cycle ;

[0128] In addition, in order to illustrate the superiority of the proposed method, wearable control experiments were carried out using the traditional ADRC method and the ADRC learning control method of the present invention. The control parameters of the ADRC learning control method are set as follows: , , , , , ;

[0129] Figure 2-Figure 5 It is a joint trajectory tracking control effect diagram based on two control methods. It can be seen from the experimental results that the control method proposed by the present invention not only has good robustness, but also has a smaller joint trajectory tracking error than the traditional anti-disturbance control method as the control operation time goes on. The control accuracy is improved by 0.08rad compared with the traditional anti-disturbance control method.

[0130] Figure 6 This is the observation effect of the linear extended state observer based on the self-disturbance rejection learning control. It can be seen from the figure that the extended state observer can well estimate the unknown disturbance and system state;

[0131] In summary, the rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method of this embodiment has good robustness and stability, can control the system tracking error at a low level, and has great application prospects for improving the control performance of the rope-driven lower limb rehabilitation exoskeleton.

[0132] The above combined with the drawings and embodiments demonstrates the superiority of the method designed by the present invention, but the present invention is not limited to the above implementation mode. Various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. A rope-driven lower limb rehabilitation exoskeleton self-disturbance rejection learning control method, characterized in that the method comprises the following steps: Step 1: Analyze the relationship between the motor driving torque and the joint control torque, and establish a dynamic model of the rope-driven lower limb rehabilitation exoskeleton; Step 2: Design the sliding surface to avoid the error amplification effect of the differential velocity signal; Step 3: Design an anti-disturbance learning controller and analyze system performance to achieve trajectory tracking control of the lower limb rope-driven rehabilitation exoskeleton. The process of step 1 is as follows: 1.1 Establishment of the double-lasso transmission system model. (1)； In formula (1), Indicates the initial preload of the Bowden rope in the double lasso system; express The driving torque at the motor end at the moment; and Respectively The control torque at the exoskeleton joints at the moment and the previous moment; They represent the radii of the motor-end driving wheel and the exoskeleton joint driving wheel respectively; It is a sign function, which is defined as positive when the transmission is clockwise, negative when the transmission is counterclockwise, and zero when there is no transmission; is the Coulomb friction coefficient between the bushing and the Bowden cable; represents the curvature of the lasso element, is the casing length; 1.2 Dynamic modeling of lower limb exoskeleton, (2)； In formula (2), Respectively represent the angle, angular velocity and angular acceleration vector of each joint of the exoskeleton; is a symmetric positive definite inertia matrix, is the Coriolis force and centripetal force matrix, is the gravity matrix; Indicates the joint friction torque generated by the motor reducer and mechanism installation; represents the human-computer interaction torque; The lower limb exoskeleton joints and the driving motors are driven by lassoes. Combining formula (1) and formula (2), the dynamic model of the rope-driven lower limb rehabilitation exoskeleton is: (3)； In formula (3), ; 1.3 Defining state variables , , the state space expression of the exoskeleton system is, (4)； In formula (4), Respectively The first derivative of ; In addition, given the period is Smooth bounded trajectory of , there is an expected input satisfy, (5)； In formula (5), is a bounded periodic signal, Respectively The first-order derivative of ; combined with equation (5), the system state space expression (4) becomes, (6)； In formula (6), ; ; The process of step 2 is as follows: 2.1 Calculation of system trajectory tracking error , (7)； 2.2 Design of sliding surface , (8)； In formula (8), is an adjustable parameter; yes An estimated value of yes The first derivative of ; express The observation error of The process of step 3 is as follows: 3.1 Define the controller, (9)； In formula (9), For expected input The estimated value of is the robust control term; 3.2 Designing the Law of Repeated Learning Estimate the periodic uncertainty in system (6), (10)； In formula (10), and Respectively exist and Estimated value of the moment; for repeated learning gains; is the limiting function, defined as, (11)； In formula (11), express The limit value of is a symbolic function; In addition, in formula (10) For definition in A continuous function on (12)； 3.3 Design an extended state observer to estimate the unknown state of the system. To this end, rewrite equation (6) as follows: (13)； In formula (13), ,in yes The inverse matrix of , express The estimation error of It is the known part of the system, obtained through prior knowledge; express The first derivative of is a bounded function; For the system described by equation (13), the linear extended state observer is designed as: (14)； In formula (14), Represent the observer state The first derivative of ; represents the bandwidth constant; 3.4 Design of Active Disturbance Rejection Controller Compensating for non-periodic uncertainties in the system, (15)； In formula (15), is an adjustable parameter; Substituting equation (15) into equation (9), the ADRC is: (16)； 3.5 Constructing Lyapunov functions , analyze system performance, (17)； Derivative of formula (17) yields: (18)； In formula (18), Respectively The first derivative of ; and Respectively exist and The estimated error at the moment; based on the inequality , And the nature ,in , represents any real number; there is, (19)； In formula (19), express The first derivative of ; is a normal number, satisfying , express The observation error, ; is a bounded parameter, ; , ; when hour, established, so Finally converges to the interval ,at this time, (20)； It can be seen that the system is uniformly bounded and the tracking error It eventually converges to a region near zero.

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