Robust control method for exoskeleton based on predetermined time stabilization

Abstract

A kind of exoskeleton robust control method based on predetermined time stability belongs to the field of robot control technology, including the following steps: step one, establish the dynamics model of degree of freedom exoskeleton robot;Step two, establish predetermined time stability criterion;Step three, based on the predetermined time stability criterion, design predetermined time disturbance observer quickly estimate model uncertainty in system and unknown human-robot interaction;Step four, combined with predetermined time disturbance observer, based on the predetermined time stability criterion, develop predetermined time controller, ensure that the trajectory tracking error of exoskeleton converges to a small area near zero within predetermined time.This application can meet the requirements of fast convergence and high robustness of exoskeleton system, compared with limited / fixed time control, its convergence time can be directly determined by two parameters, and effectively solve the initial control input problem of predetermined time control, more conducive to practical engineering application and promotion.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, specifically relating to a robust control method for an exoskeleton based on predetermined time stability. Background Technology

[0002] In recent years, the effectiveness of exoskeleton robot-assisted rehabilitation has been fully validated in numerous clinical practices and studies, and it has gradually entered the commercialization process. Compared with traditional manual rehabilitation, exoskeleton robots can provide repetitive, sustainable, high-intensity training, quantitatively assess patients' rehabilitation effects, and thus improve patients' rehabilitation efficiency.

[0003] Exoskeleton robot-assisted rehabilitation strategies are generally divided into passive and active modes. In passive mode, trajectory tracking control is the primary control method for exoskeleton-assisted rehabilitation and the foundation for other control strategies. To improve the tracking performance of exoskeleton robots, different control methods have been proposed and applied, such as PID control, adaptive control, sliding mode control, fuzzy control, and neural networks. However, these methods can only achieve asymptotic convergence of tracking errors and cannot meet the rapid response requirements of exoskeleton systems.

[0004] To improve the tracking speed of exoskeletons, patent CN 116807829A discloses a control method for a lower limb rehabilitation exoskeleton robot based on super-twisted end sliding mode, achieving finite-time convergence of tracking errors based on finite-time stability. However, the upper bound of the convergence time in finite-time control heavily depends on the initial state of the system; when the initial state is too large, the requirement for rapid response of the exoskeleton cannot be met. To address this, patents CN 120480896A and CN 120572533A respectively disclose a multi-level control method for lower limb exoskeletons and a fixed-time control method for exoskeleton robots based on output constraints and interference observation. These methods, based on fixed-time control theory, enable the tracking error to converge within a fixed time, independent of the initial state of the system. However, the estimation of the upper bound of the convergence time by the fixed-time stable control method is extremely conservative. Recently, predetermined-time control has been proposed, where the minimum upper bound of the convergence time can be determined by adjusting a control parameter setting, independent of the initial state of the system. Patent CN 120170744A discloses an adaptive sliding mode control method for a robotic arm based on predetermined time stability. This method guarantees that the tracking error of the robotic arm will converge within a set time, provided the derivative of the Lyapunov function satisfies the proposed predetermined time stability criterion. However, the controller designed based on this criterion exhibits a positive correlation between its initial control input and the initial error. As the initial error increases, the initial control input increases dramatically. Excessive initial control input can shorten the lifespan of the exoskeleton actuator or even cause it to malfunction, even with saturation protection for the control input.

[0005] Furthermore, due to factors such as model uncertainty and human-computer interaction, improving the robustness of the control system helps enhance the reliability and safety of the exoskeleton. Disturbance observers are an effective means of real-time estimation and compensation for unknown disturbances. However, traditional disturbance observers have a slow convergence speed in estimating errors. When the exoskeleton is accelerated / decelerated or goes up / down stairs, the slow estimation may lead to control oscillations or even instability, affecting user safety.

[0006] Therefore, considering the initial input problem, constructing a new predetermined time stability criterion, and developing a predetermined time robust control method for exoskeleton robots based on this criterion, has significant research significance and application value. Summary of the Invention

[0007] To overcome the shortcomings of existing technologies, this invention proposes a new predetermined time stability criterion. Based on this criterion, a robust control method for exoskeleton based on predetermined time stability is provided, which enables the trajectory tracking error of the exoskeleton to converge to a small region near zero within a predetermined time. The proposed control framework incorporates a predetermined time disturbance observer to quickly estimate and compensate for unknown uncertainties and human-computer interaction forces in the exoskeleton system, effectively improving the robust stability of the system.

[0008] The technical solution of this invention is: A robust control method for an exoskeleton based on predetermined time stability includes the following steps: Step 1: Establish Dynamic model of a degree-of-freedom exoskeleton robot; Step 2: Establish a stability criterion for the predetermined time; Step 3: Based on the predetermined time stability criterion, design a predetermined time disturbance observer to quickly estimate the model uncertainty and unknown human-computer interaction force in the system; Step 4: Combine the predetermined time perturbation observer and develop a predetermined time robust controller based on the predetermined time stability criterion to ensure that the trajectory tracking error of the exoskeleton converges to a small region near zero within a predetermined time.

[0009] Furthermore, the process of step one is as follows: consider The dynamic model of the degree-of-freedom exoskeleton robot is established as follows: (1); in, , and These represent the angle, angular velocity, and angular acceleration vectors of the exoskeleton joints, respectively. and These represent the nominal and uncertain parts of the positive definite inertia matrix, respectively. and These represent the nominal and uncertain parts of the Coriolis force and centripetal force matrices, respectively. and These represent the nominal and uncertain parts of the gravity matrix, respectively. Indicates the unknown human-computer interaction torque. This indicates the control input torque.

[0010] Furthermore, the process of step two is as follows: A time-stability criterion is established if a positive definite Lyapunov function exists. Conditions met: (2); in, yes Regarding time The first derivative; Predetermined time constant , , It is a natural constant, a positive real number. , If the value is pi, then the system is globally time-stable, and the lowest upper bound of the stable time is... .

[0011] Furthermore, the process of step three is as follows: definition , and Based on the exoskeleton model (1), an auxiliary system is constructed: (3); in, , These are the state variables of the auxiliary system (3). They represent Regarding time First and second derivatives, adjustable parameters ; Then, design a perturbation observer with a predetermined time: (4); in, It is a concentrated disturbance The estimated value, express Regarding time The first derivative, yes The estimated value.

[0012] Preferred, The update formula is designed as follows: (5); in, express Regarding time The first derivative, , , , , Represents a symbolic function.

[0013] The process of step four is as follows: Define tracking error and intermediate error : (6); in, It is the expected joint trajectory of the exoskeleton; This represents a virtual control input, designed as follows: (7); in, yes Regarding time The first derivative, real numbers , , .

[0014] Furthermore, combining the disturbance observer (4), the predetermined time robust controller is designed based on the backstepping technique as follows: (8); Among them, real numbers , , , It is a virtual control input Regarding time The first derivative, positive real number The value of satisfies , This represents the L2 norm.

[0015] The technical concept of this invention is: To address the rapid response requirements of exoskeleton robots, a pre-time control theory is considered for developing an exoskeleton controller. However, the initial control torque of the controller designed based on the existing pre-time stability criterion is positively correlated with the initial error. As the initial error increases, a larger initial control torque is required, which can lead to a shortened exoskeleton lifespan or even loss of control. To address this, this invention proposes a new pre-time stability criterion to solve the problem of initial control torque. Based on this criterion, a pre-time robust controller is developed for uncertain exoskeleton systems, ensuring that the trajectory tracking error of the exoskeleton converges to a small region near zero within a predetermined time. Simultaneously, to improve the robustness of the exoskeleton system, a pre-time perturbation observer is designed based on this criterion to quickly estimate and compensate for unknown uncertainties and human-robot interaction forces in the exoskeleton system.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. This invention proposes a new predetermined time stability criterion. The predetermined time controller designed based on this criterion effectively solves the problem of excessive initial control input and is more conducive to practical engineering applications. 2. This invention provides a robust control method based on the proposed predetermined time stability criterion. This method ensures that the trajectory tracking error of the exoskeleton converges to a small region near zero within a predetermined time, thus meeting the rapid response requirements of the exoskeleton system. Compared to finite / fixed time control, its convergence time can be preset according to actual needs and does not depend on the initial state of the system. 3. Based on the proposed predetermined time stability criterion, this invention designs a predetermined time perturbation observer to estimate the model uncertainty and unknown human-computer interaction force in the exoskeleton system, ensuring the rapid and accurate convergence of estimation errors and improving the robust stability of the system. Attached Figure Description

[0017] Figure 1 This is the control principle diagram of the present invention; Figure 2 The controller proposed in this invention operates at a predetermined time. Error convergence effect diagram at time; Figure 3 The controller proposed in this invention operates at a predetermined time. Error convergence effect diagram at time; Figure 4 It is the scheduled time A schematic diagram of trajectory tracking using different controllers; Figure 5 It is the initial position. Comparison of control inputs for different controllers; Figure 6 It is the initial position. A comparison chart of control inputs for different controllers. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments, but this is not intended to limit the scope of protection of the present invention.

[0019] Reference Figures 1-6 A robust control method for an exoskeleton based on predetermined time stability includes the following steps: Step 1: Establish Dynamic model of a degree-of-freedom exoskeleton robot: (1); in, ; and These represent the angle, angular velocity, and angular acceleration vectors of the exoskeleton joints, respectively. and These represent the nominal and uncertain parts of the positive definite inertia matrix, respectively. and These represent the nominal and uncertain parts of the Coriolis force and centripetal force matrices, respectively. and These represent the nominal and uncertain parts of the gravity matrix, respectively. Indicates the unknown human-computer interaction torque. Indicates the control input torque; Step 2: Establish a stability criterion for the predetermined time, as follows: For general nonlinear systems, if there exists a positive definite Lyapunov function... satisfy (2); in, yes Regarding time The first derivative; Predetermined time constant , , It is a natural constant, a positive real number. , If the value is pi, then the system is globally time-stable, and the lowest upper bound of the stable time is... .

[0020] Step 3: Based on the predetermined time stability criterion, design a predetermined time perturbation observer to quickly estimate the model uncertainty and unknown human-computer interaction force in the system. The process is as follows: definition , and Based on the exoskeleton model (1), an auxiliary system is constructed: (3); in, , These are the state variables of the auxiliary system (3). They represent Regarding time First and second derivatives, adjustable parameters ; Then, design a perturbation observer with a predetermined time: (4); in, It is a concentrated disturbance The estimated value, express Regarding time The first derivative, yes The estimated value; The update formula is designed as follows: (5); in, express Regarding time The first derivative, , , , , Represents a symbolic function; Estimation performance analysis of the pre-defined time perturbation observer (4); Define the Lyapunov function: (9); Differentiate formula (9) and substitute formula (6) into it: (10); According to criterion formula (2) and formula (10), the error At the scheduled time It converges to zero; Combining formulas (3), (4), and (5), calculate the disturbance estimation error: (11); Therefore, the perturbation estimation error Also at the scheduled time It converges to zero, thus quickly achieving an accurate estimate of concentrated disturbances; Step 4: Combine the predetermined time perturbation observer with the predetermined time stability criterion to develop a predetermined time robust controller, ensuring that the trajectory tracking error of the exoskeleton converges to a small region near zero within a predetermined time. The process is as follows: Define tracking error and intermediate error : (6); in, It is the expected joint trajectory of the exoskeleton; This represents a virtual control input, designed as follows: (7); in, yes Regarding time The first derivative, real numbers , , ; Combining the disturbance observer (4), and based on the backstepping technique, the predetermined time robust controller is designed as follows: (8); Among them, real numbers , , , It is a virtual control input Regarding time The first derivative, positive real number The value of satisfies , Represents the L2 norm; Stability and convergence analysis of tracking error of closed-loop system under the action of controller (8); Define the Lyapunov function: (12); Differentiate formula (12) and substitute formulas (1)(6)(7)(8) into it: (13); because Substitute and The definition of , formula (13) can be scaled down to: (14); According to criterion formulas (2) and (14), the tracking error At the scheduled time It converges to a small region near zero.

[0021] To verify the effectiveness of the method proposed in the embodiments, the present invention used the MATLAB simulation platform to simulate and verify the control effect of the predetermined time robust controller described in formula (8). Figure 1 This is a control principle diagram of the method proposed in this invention.

[0022] Consider a 1-DOF exoskeleton robot system, corresponding to the dynamic model (1): , , ,in , , , Uncertainty value Unknown human-computer interaction force .

[0023] Select the desired trajectory for exoskeleton shutdown The simulation sampling time is 0.001s, and the controller parameters are selected as follows: , , , , Two different booking times were selected, namely and ;when When, select , ;when When, select , The initial values ​​for the exoskeleton joint angles are set as follows: and The initial value of the joint angular velocity is set to .

[0024] To demonstrate the superiority of the method proposed in the embodiments, a predetermined time robust controller (M1) is designed based on the predetermined time stability criterion proposed in CN120170744A under the same concept. The difference between this controller and the controller (M2) proposed in this invention is that... ,at this time The value is .

[0025] Figure 2 and Figure 3 The convergence performance of the control method proposed in this invention at different predetermined times is described. It can be seen that the angle tracking error... intermediate error and estimation error All can be at the scheduled time The convergence to a small region near the origin indicates that the proposed control method performs well in terms of speed, stability, accuracy, and robustness.

[0026] Figure 4 The figure shows a trajectory tracking diagram of controllers M1 and M2 developed based on the predetermined time stability criterion proposed in CN120170744A and the predetermined time stability criterion proposed in this invention, under the same technical approach. As shown in the figure, both controllers can ensure that the exoskeleton tracks the desired trajectory within a predetermined time.

[0027] Figure 5 and Figure 6 A comparison of the control inputs of two controllers is presented. It can be found that the initial control input of controller M1, designed based on the predetermined time stability criterion proposed in CN120170744A, is highly sensitive to the initial position. When the initial error increases, the initial control input surges. In contrast, controller M2, designed based on the predetermined time stability criterion proposed in this invention, has a very small initial control input regardless of how the initial position changes. This perfectly solves the problem of initial input in traditional predetermined time control and is more conducive to practical engineering applications.

[0028] The embodiments described in this specification are merely examples of implementations of the inventive concept and are for illustrative purposes only. The scope of protection of this invention should not be considered limited to the specific forms described in these embodiments; rather, it extends to equivalent technical means conceived by those skilled in the art based on the inventive concept.

Claims

1. A robust control method for an exoskeleton based on predetermined time stability, characterized in that, Includes the following steps: Step 1: Establish The dynamic model of the degree-of-freedom exoskeleton robot is as follows: consider The dynamic model of the degree-of-freedom exoskeleton robot is established as follows: （1）； in, , and These represent the angle, angular velocity, and angular acceleration vectors of the exoskeleton joints, respectively. and These represent the nominal and uncertain parts of the positive definite inertia matrix, respectively. and These represent the nominal and uncertain parts of the Coriolis force and centripetal force matrices, respectively. and These represent the nominal and uncertain parts of the gravity matrix, respectively. Indicates the unknown human-computer interaction torque. Indicates the control input torque; Step 2, the process of establishing the stability criterion for the predetermined time is as follows: A time-stability criterion is established if a positive definite Lyapunov function exists. Conditions met: （2）； in, yes Regarding time The first derivative; Predetermined time constant , , It is a natural constant, a positive real number. , If the value is pi, then the system is globally time-stable, and the lowest upper bound of the stable time is... ; Step 3: Based on the predetermined time stability criterion, the predetermined time perturbation observer is designed to quickly estimate the model uncertainty and unknown human-computer interaction force in the system. The process is as follows: definition , and Based on the exoskeleton model (1), an auxiliary system is constructed: （3）； in, , These are the state variables of the auxiliary system (3). They represent Regarding time First and second derivatives, adjustable parameters ; Then, design a perturbation observer with a predetermined time: （4）； in, It is a concentrated disturbance The estimated value, express Regarding time The first derivative, yes The estimated value; The update formula is designed as follows: （5）； in, express Regarding time The first derivative, , , , , Represents a symbolic function; Step 4: Combine the predetermined time perturbation observer and develop a predetermined time robust controller based on the predetermined time stability criterion to ensure that the trajectory tracking error of the exoskeleton converges to a small region near zero within a predetermined time.

2. The robust control method for an exoskeleton based on predetermined time stability as described in claim 1, characterized in that, The process of step four is as follows: Define tracking error and intermediate error : （6）； in, It is the expected joint trajectory of the exoskeleton; This represents a virtual control input, designed as follows: （7）； in, yes Regarding time The first derivative, real numbers , , .

3. The robust control method for an exoskeleton based on predetermined time stability as described in claim 2, characterized in that, In step four, combined with the disturbance observer (4), the predetermined time robust controller is designed based on the backstepping technique as follows: （8）； Among them, real numbers , , , It is a virtual control input Regarding time The first derivative, positive real number The value of satisfies , This represents the L2 norm.

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