Design method of barrier function rehabilitation robot safety tracking control system

Abstract

The invention discloses a design method of a barrier function rehabilitation robot safety tracking control system, and relates to the technical field of medical robots. The method comprises the steps that on the basis of an existing double-joint single-arm robot mathematical model, a mathematical model with uncertain model parameters, uncertain external disturbance and uncertain external force borne by the tail end is established, and the established model is closer to a real model of a rehabilitation robot; the uncertainty in the model is classified into one class, and a disturbance observer is used for estimating and compensating the uncertainty; a logarithmic obstacle Lyapunov function is adopted to constrain the joint angle; and designing an adaptive trajectory tracking controller based on the disturbance observer and the obstacle Lyapunov function method, and tracking a set trajectory. The high-precision tracking of the target trajectory is ensured, the actual motion trajectory always moves within a certain range on the two sides of the target trajectory, and the secondary injury of the patient in the rehabilitation process is avoided.

Description

Technical Field

[0001] The present application relates to the technical field of medical robots, and in particular to a design method for a safety tracking control system of an obstacle function rehabilitation robot. Background Art

[0002] With the rapid development of technologies such as artificial intelligence and the Internet of Things, international scholars have identified rehabilitation robots that reconstruct limb motor function as a key research area, particularly in robotic motion control strategies and methods. The emergence of rehabilitation robots not only improves the therapeutic effectiveness of rehabilitation therapists but also reduces their workload. Developed countries such as Europe and the United States have invested heavily in research, development, and promotion of rehabilitation robots, enhancing the technical experience of rehabilitation robots and making them more widely available. Because the distal end of the rehabilitation robot's robotic arm directly contacts the patient, ensuring patient safety during treatment is crucial to the design of motion control systems. Establishing an accurate mathematical model of the system is essential for achieving precise control. The primary challenge facing rehabilitation robot motion control is the accuracy of the mathematical model.

[0003] The existing mathematical model has a large deviation from the ideal model. Using the established nominal mathematical model to design a controller will cause insufficient control accuracy, which can easily cause secondary harm to patients.

[0004] Therefore, it is urgent to design a tracking control method to avoid secondary injuries to patients during the rehabilitation process. Summary of the Invention

[0005] Based on this, it is necessary to provide a design method for a safe tracking control system of an obstacle function rehabilitation robot to address the above technical problems and design a tracking control system to avoid secondary injuries to patients during the rehabilitation process.

[0006] The present invention adopts the following technical solutions: The present invention provides a design method for a safety tracking control system of an obstacle function rehabilitation robot, comprising: Based on the existing mathematical model of a dual-joint single-arm robot, a mathematical model of a rehabilitation robot including multiple uncertainties is established; The multiple uncertain factors are combined into one item and variable conversion is performed to obtain a mathematical model of the rehabilitation robot after the variable conversion; a disturbance observer is designed based on the mathematical model of the rehabilitation robot after the variable conversion; the disturbance observer is used to observe the combined uncertain factors; Through the constant constraint boundary conditions of the rehabilitation robot's position error, an obstacle Lyapunov function is designed to constrain the motion trajectory of the rehabilitation robot; combining the disturbance observer system and the obstacle Lyapunov function, an adaptive trajectory tracking controller is designed, and through the virtual control rate of the adaptive trajectory tracking controller, the rehabilitation robot's mechanical arm is controlled within the range of the preset target trajectory.

[0007] Preferably, the mathematical model of the rehabilitation robot including uncertainty factors is: ; in, ; Where, q is the joint angle, is the combined term of uncertain factors, is the inertia matrix, and , is the Coriolis centripetal matrix, , represents the gravity matrix, is the joint angle, represents the control input vector to be designed; , , are the uncertainty factors in the inertia matrix, Coriolis centripetal matrix and gravity matrix, is the Jacobian matrix, is the external force acting on the end of the robotic arm.

[0008] Preferably, the mathematical model formula of the rehabilitation robot after variable conversion is: ; in, .

[0009] Preferably, a disturbance observer system is designed, specifically comprising: The mathematical model of the rehabilitation robot after variable conversion is rewritten into the form of state space, and the formula is: ; According to the mathematical model of the rehabilitation robot in the state space form, the disturbance observer is designed, and the formula is: ; Where, , represents the observer gain, is the state of the observer, is the observed value of the system uncertainty factor, , is the defined observation error.

[0010] Preferably, the formula of the barrier Lyapunov function is: ; Where, V 1 is the barrier Lyapunov function, k qi is the constant constraint boundary condition of the rehabilitation robot position error, , , is the square term of the position error.

[0011] Preferably, the disturbance observer system and the obstacle Lyapunov function are combined to design an adaptive trajectory tracking controller, which specifically includes: Barrier Lyapunov function The derivative is: ; The speed error of the rehabilitation robot is ,in, is the virtual control rate, for position error The derivative is: ; Defining virtual control laws , the formula is: ; Where, is the derivative of the desired position, A is the position error matrix; in, ; in, , is a positive constant; Substitute the derived position error and virtual control law into the derived obstacle Lyapunov function: ; According to the mathematical model of the rehabilitation robot after variable conversion, the velocity error is derived as follows: ; in, For uncertainty factors; The disturbance observer is used to compensate for the uncertainty factors of the system. The formula is: ; According to Lyapunov stability theory, an adaptive trajectory tracking controller is designed, and the formula is: ; Where, Is a positive number.

[0012] Preferably, the virtual control rate is set and input into the adaptive trajectory tracking controller to control the rehabilitation robot arm within the range of the preset target trajectory, specifically including: Set the virtual control rate according to the preset motion trajectory range; Inputting the virtual control rate, the joint angle, the preset speed and the preset position of the rehabilitation robot arm into the adaptive trajectory tracking controller; The adaptive trajectory tracking controller controls the rehabilitation robot arm to assist the patient in performing rehabilitation exercises within a preset motion trajectory.

[0013] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects: Based on the existing mathematical model of a dual-joint single-arm rehabilitation robot, the present invention establishes a mathematical model containing model uncertainty factors. Combined with the estimation capability of the disturbance observer, the model is closer to the internal and external action mechanisms during the operation of the actual robot, thereby improving the accuracy of the controller designed based on the model; by proposing a new logarithmic time-invariant obstacle function, which is different from the existing time-invariant logarithmic obstacle function, the proposed obstacle function can not only handle systems with constraint requirements but also design controllers for systems without constraint requirements; an adaptive tracking controller is designed based on the position constraint control of the rehabilitation robot based on the obstacle Lyapunov function and combined with the disturbance observer. While ensuring high-precision tracking of the target trajectory, the actual motion trajectory of the robot's manipulator always moves within a certain range on both sides of the target trajectory, avoiding secondary injuries to patients during the rehabilitation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0015] Figure 1 A schematic flow chart of a design method for a safety tracking control system for an obstacle function rehabilitation robot provided by the present invention; Figure 2 A diagram of the architecture of a closed-loop control system for a design method of a safety tracking control system for an obstacle function rehabilitation robot provided by the present invention; Figure 3 A schematic diagram of an obstacle Lyapunov function for a design method of a safety tracking control system for an obstacle function rehabilitation robot provided by the present invention; Figure 4 A diagram showing the tracking effect of joint 1 based on a new obstacle Lyapunov function under an undisturbed observer (constraints are bounded) in a design method for a safe tracking control system for an obstacle function rehabilitation robot provided by the present invention; Figure 5 A diagram showing the joint 2 tracking effect (constrained and bounded) based on a new obstacle Lyapunov function under undisturbed observer compensation in a design method for a safe tracking control system for an obstacle function rehabilitation robot provided by the present invention; Figure 6 A design method for a safe tracking control system for an obstacle function rehabilitation robot is shown in the figure of joint 1 tracking effect based on a new obstacle Lyapunov function under a disturbance observer (constraint is infinite); Figure 7 A design method for a safe tracking control system for an obstacle function rehabilitation robot is shown in the figure of joint 2 tracking effect based on a new obstacle Lyapunov function with disturbance observer compensation (constraint infinity); Figure 8 This is a diagram showing the effect of the disturbance observer designed for the design method of a safe tracking control system for an obstacle function rehabilitation robot on the estimation of the overall disturbance of the system. DETAILED DESCRIPTION

[0016] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments in the specification, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0017] The following describes in detail the technical solutions provided by various embodiments of the present application in conjunction with the accompanying drawings.

[0018] Figure 1 The flowchart of the design method of a safety tracking control system for an obstacle function rehabilitation robot in the present invention specifically includes the following steps: S101: Establish a mathematical model of a rehabilitation robot including multiple uncertainty factors.

[0019] Establish a mathematical model of the rehabilitation robot including uncertainty factors, including: When the end of the robotic arm is not subject to external force, the mathematical model of the existing dual-joint single-arm robot is as follows: (1); Where, is the inertia matrix, and , is the Coriolis centripetal matrix, represents the gravity matrix, is the joint angle, represents the control input vector to be designed; Based on the existing mathematical model of the dual-joint single-arm robot, a mathematical model of the rehabilitation robot including uncertainty factors is established. The formula is: (2); Where, , , Corresponding to the uncertainty factors in the inertia matrix, Coriolis centripetal matrix and gravity matrix, is the Jacobian matrix, is the external force acting on the end of the robotic arm.

[0020] Among them, the uncertainty factors include: parameter uncertainty, external disturbance uncertainty and external force uncertainty at the end.

[0021] S102: Combining the multiple uncertain factors into one item and performing variable conversion to obtain a mathematical model of the rehabilitation robot after variable conversion; designing a disturbance observer based on the mathematical model of the rehabilitation robot after variable conversion; the disturbance observer is used to observe the combined uncertain factors.

[0022] The uncertain factors are combined into one item and variable transformation is performed, including: set up is a combined term of uncertain factors, then: (3); Substitute (3) into the mathematical model of the rehabilitation robot including uncertainty factors: (4); Perform variable transformation on formula (4): (5); Substituting (5) into (4), we can obtain the mathematical model of the rehabilitation robot after variable conversion: (6); in, (7).

[0023] Design a disturbance observer system to observe the combined uncertainty factors, including: Rewrite Equation (6) into the form of state space, the formula is: (8); According to formula (8), the disturbance observer system is designed, and the formula is: (9); Where, represents the observer gain, is the state of the observer, is the observed value of the system uncertainty factor, , is the defined observation error.

[0024] S103: Through the constant constraint boundary conditions of the rehabilitation robot's position error, an obstacle Lyapunov function is designed to constrain the motion trajectory of the rehabilitation robot; combining the disturbance observer system and the obstacle Lyapunov function, an adaptive trajectory tracking controller is designed, and by setting the virtual control rate of the adaptive trajectory tracking controller, the rehabilitation robot's manipulator arm is controlled within the range of the preset target trajectory.

[0025] Optionally, by setting a virtual control rate and inputting it into an adaptive trajectory tracking controller, the rehabilitation robot arm is controlled within the range of a preset target trajectory, specifically including: setting the virtual control rate according to a preset motion trajectory range; inputting the virtual control rate, the joint angle, preset speed and preset position of the rehabilitation robot arm into the adaptive trajectory tracking controller; the adaptive trajectory tracking controller controls the rehabilitation robot arm to assist the patient in rehabilitation exercises within the preset motion trajectory range.

[0026] Optionally, the obstacle Lyapunov function is designed based on the constant constraint boundary conditions of the rehabilitation robot position error, specifically including: setting the target trajectory to , according to the target trajectory, the position error is defined as , the position error satisfies the constant constraint boundary condition ,in, .

[0027] Optionally, through the constant constraint boundary condition, the barrier Lyapunov function is designed to be: (10); Wherein, the barrier Lyapunov function satisfies the inequality condition: (11); (12).

[0028] Where, , , is the square term of the position error.

[0029] Alternatively, according to the inequality condition, when the constraint boundary is infinite, that is, when the position of the robot is unconstrained, according to the edge clamp theorem, we can get: (13); According to formula (13), the barrier Lyapunov function is ensured The boundedness of is used to control the motion trajectory of the rehabilitation robot.

[0030] Barrier Lyapunov function The derivative is: (14); Set the speed error of the rehabilitation robot to ,in, is the virtual control rate, for position error The derivative is: (15); Defining virtual control laws , the formula is: (16); in, (17); in, , is a positive constant.

[0031] Substitute equations (15) and (16) into equation (14): (18); According to formula (6), the velocity error is derived as follows: (19); in, For uncertainty factors.

[0032] The disturbance observer is used to compensate for the uncertainty factors of the system, specifically: (20); According to Lyapunov stability theory, an adaptive trajectory tracking controller is designed, and the formula is: (twenty one); Where, Is a positive number.

[0033] Through the above method steps, the stability of the designed dual-joint single-arm robot motion control system is proved.

[0034] Choose the second candidate barrier Lyapunov function: (twenty two); right Taking the derivative we get: (twenty three); Substitute equation (19) into equation (23): (twenty four); Assuming that the system uncertainty factor is a slowly changing signal, the observation value of the observer system uncertainty factor is derived: (25); Substitute equations (21) and (25) into equation (24): (26); According to the inequality condition (11) and the selected parameters satisfy and , Equation (26) is rewritten as: (27); in, (28) ; Solving differential equations have to: (29); According to the definition of the obstacle Lyapunov function, the conversion formula is: (30); Derived , both ,according to , further deducing that the robot position trajectory satisfies the constraint conditions .

[0035] According to the inequality condition (11), we can get: (31); It is deduced that the tracking error of the rehabilitation robot system satisfies the following conditions: (32); Position error of the robot system , speed error and uncertainties The equilibrium point is reached and the position trajectory of the dual-joint single-arm robot remains within the preset trajectory range.

[0036] In summary, rehabilitation robots are an important branch of medical robotics, involving many fields such as computer science, robotics, control science and engineering, biomechanics, and mechanical mechanics. The mathematical model of rehabilitation robots is complex, and the existing mathematical model is only a nominal model. Based on the existing mathematical model of a dual-joint single-arm robot, a mathematical model with uncertainty in model parameters, uncertainty in external disturbances, and uncertainty in the external forces acting on the end-point is established. This model is closer to the actual model of the rehabilitation robot, thereby improving the accuracy of motion control. Then, to better approximate the actual model, the uncertainties in the established model are classified into one category, and a disturbance observer is used to estimate and compensate for them, thereby improving the adaptability and robustness of the dual-joint single-arm rehabilitation robot's motion control system. At the same time, due to the physical characteristics of the rehabilitation robot and the contact distance between the end-point and the patient, the joint angles of the rehabilitation robot must be constrained within a certain range. Therefore, a new logarithmic barrier Lyapunov function is used to effectively constrain the joint angles to ensure the safety of the rehabilitation robot's operation. Finally, an adaptive trajectory tracking controller is designed based on the disturbance observer and the barrier Lyapunov function method to achieve high-precision tracking of the set trajectory.

[0037] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.

Claims

1. A design method for a safe tracking control system for an obstacle function rehabilitation robot, characterized in that: include: Establish a mathematical model of rehabilitation robots including multiple uncertainties; The multiple uncertain factors are combined into one item and variable conversion is performed to obtain a mathematical model of the rehabilitation robot after the variable conversion; a disturbance observer is designed based on the mathematical model of the rehabilitation robot after the variable conversion; the disturbance observer is used to observe the combined uncertain factors; By using the constant constraint boundary conditions of the rehabilitation robot's position error, an obstacle Lyapunov function is designed to constrain the motion trajectory of the rehabilitation robot; an adaptive trajectory tracking controller is designed by combining the disturbance observer system and the obstacle Lyapunov function; By setting the virtual control rate of the adaptive trajectory tracking controller, the rehabilitation robot arm is controlled within the range of the preset target trajectory.

2. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 1, characterized in that: The mathematical model of the rehabilitation robot including uncertainty factors is: ； in, ； Where, q is the joint angle, is the combined term of uncertain factors, is the inertia matrix, and , is the Coriolis centripetal matrix, , represents the gravity matrix, is the joint angle, represents the control input vector to be designed; , , are the uncertainty factors in the inertia matrix, Coriolis centripetal matrix and gravity matrix, is the Jacobian matrix, is the external force acting on the end of the robotic arm.

3. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 2, characterized in that: The mathematical model formula of the rehabilitation robot after the variable conversion is: ； in, 。 4. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 3, characterized in that: The design of the disturbance observer system specifically includes: The mathematical model of the rehabilitation robot after variable conversion is rewritten into the form of state space, and the formula is: ； According to the mathematical model of the rehabilitation robot in the state space form, the disturbance observer is designed, and the formula is: ； Where, , represents the observer gain, is the state of the observer, is the observed value of the system uncertainty factor, , is the defined observation error.

5. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 1, characterized in that: The formula of the barrier Lyapunov function is: ； Where, V 1 is the barrier Lyapunov function, k qi is the constant constraint boundary condition of the rehabilitation robot position error, , , is the square term of the position error.

6. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 1, characterized in that: The method combines the disturbance observer system and the obstacle Lyapunov function to design an adaptive trajectory tracking controller, which specifically includes: Barrier Lyapunov function The derivative is: ； The speed error of the rehabilitation robot is ,in, is the virtual control rate, for position error The derivative is: ； Defining virtual control laws , the formula is: ； Where, is the derivative of the desired position, A is the position error matrix; in, ； in, , is a positive constant; Substitute the derived position error and virtual control law into the derived obstacle Lyapunov function: ； According to the mathematical model of the rehabilitation robot after variable conversion, the velocity error is derived as follows: ； in, For uncertainty factors; The disturbance observer is used to compensate for the uncertainty factors of the system. The formula is: ； According to Lyapunov stability theory, an adaptive trajectory tracking controller is designed, and the formula is: ； Where, Is a positive number.

7. The design method of a safety tracking control system for an obstacle function rehabilitation robot according to claim 1, characterized in that: The control of the rehabilitation robot arm within the range of a preset target trajectory by using the virtual control rate of the adaptive trajectory tracking controller specifically includes: Set the virtual control rate according to the preset motion trajectory range; Inputting the virtual control rate, the joint angle, the preset speed and the preset position of the rehabilitation robot arm into the adaptive trajectory tracking controller; The adaptive trajectory tracking controller controls the rehabilitation robot arm to assist the patient in performing rehabilitation exercises within a preset motion trajectory.

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