Fractional order terminal sliding mode control method and device applied to lower limb rehabilitation robot

Abstract

The invention discloses a fractional order terminal sliding mode control method and device applied to a lower limb rehabilitation robot, and the method comprises the steps: 1) building a plane rectangular coordinate system under a sagittal plane, and building a lower limb exoskeleton rehabilitation robot dynamic model based on an Euler-Lagrange equation; (2) a fractional order terminal sliding mode surface is designed for a lower limb exoskeleton rehabilitation robot system so as to meet the complex control requirement of the lower limb exoskeleton rehabilitation robot system; 3) designing an equivalent control law and a switching control law based on the lower limb exoskeleton rehabilitation robot kinetic model and the fractional order terminal sliding mode surface; 4) based on the Lyapunov stability theory, it is proved that the designed control law can achieve stable control over the lower limb exoskeleton rehabilitation robot; and 5) combining a plurality of memories, a processor and corresponding executable codes to realize fractional order terminal sliding mode control of the lower limb exoskeleton rehabilitation robot. According to the fractional order terminal sliding mode control method and device, the parameter uncertainty of dynamic modeling is considered, the design of a control system becomes more flexible, and the robustness of the control system is improved.

Description

Technical Field

[0001] The present invention belongs to the field of motion control of lower limb exoskeleton robots, and in particular relates to a fractional-order terminal sliding mode control method and device applied to a lower limb rehabilitation robot. Background Art

[0002] With the deepening of the aging of Chinese society and the increase in the number of patients with lower limb movement disorders caused by diseases such as stroke and spinal cord injury, the demand for the application of exoskeleton robots in the field of rehabilitation medicine has gradually increased. As an important tool for auxiliary movement training, lower limb exoskeleton rehabilitation robots can promote the recovery of patients' neuromuscular function through repetitive and controllable movement training. However, the existing control methods of lower limb exoskeleton rehabilitation robots, such as PID control, fuzzy control and adaptive control, have achieved effective control of the rehabilitation training process to a certain extent, but when dealing with individual differences in patients and nonlinear and time-varying biomechanical characteristics, there are still problems such as difficulty in setting control parameters and insufficient robustness.

[0003] Sliding mode control has good robustness in the face of system parameter uncertainty and external disturbances. In recent years, it has gradually become a control strategy that has attracted much attention in the field of robot control. Sliding mode control is a variable structure control method. Its main feature is the discontinuity of the control process. Its core idea is to design a sliding surface so that the system state moves back and forth with high frequency and small amplitude along the expected trajectory. This state is called "sliding mode". The sliding surface and reaching law can be designed according to the specific needs of the system. In addition, sliding mode control does not rely on the accuracy of the system model. It only requires the system to move stably on the sliding surface. Therefore, it shows good robustness in the face of parameter uncertainty, external disturbances and model nonlinearity. This feature makes it have broad application prospects in the field of exoskeleton rehabilitation robots.

[0004] In the lower limb exoskeleton rehabilitation robot system, although the traditional sliding mode control method can also achieve a certain degree of trajectory tracking control, there are still some defects in practical applications: 1) In the lower limb exoskeleton rehabilitation robot system controlled by the host computer, the robot dynamics modeling method based on the Euler-Lagrange equation cannot fully consider the complex biomechanical characteristics and environmental factors, resulting in low accuracy of the dynamics model. The system is more susceptible to modeling errors and external interference under closed-loop control, resulting in decreased control accuracy and stability; 2) When facing nonlinear and time-varying systems, traditional robot control methods have problems such as slow response speed and poor anti-interference ability, and cannot meet the high-precision gait trajectory tracking requirements in rehabilitation training.

[0005] Fractional calculus extends the traditional sense of differentiation and integration to the scope of non-integer orders, providing new mathematical tools for dealing with more complex and diverse dynamic systems. The uniqueness of fractional calculus lies in the introduction of fractional operators, which can make more detailed adjustments to the tracking performance of the system, injecting new flexibility into the design of control systems. In addition, fractional calculus operations process the global characteristics of functions in a weighted manner, which can realize the memory of function history information. This non-locality and memory characteristics enable it to more accurately describe the dynamic behavior of complex systems and have more flexible dynamic characteristics. Therefore, it is of great practical significance to introduce fractional operators under the framework of traditional sliding mode control and apply them to lower limb exoskeleton rehabilitation robot systems to overcome some limitations faced by the system. Summary of the invention

[0006] In order to overcome the above-mentioned shortcomings of the prior art and adapt to the trajectory tracking control requirements of a lower limb exoskeleton rehabilitation robot, the present invention provides a fractional-order terminal sliding mode control method and device applied to a lower limb rehabilitation robot. Compared with traditional sliding mode control, the present invention not only improves the robustness of the control system, but also makes the design of the control system more flexible.

[0007] In order to solve the above technical problems, the first aspect of the present invention relates to a fractional-order terminal sliding mode control method applied to a lower limb rehabilitation robot, comprising the following steps:

[0008] Step 1: Establish a plane rectangular coordinate system under the sagittal plane, and establish a dynamic model of the lower limb exoskeleton rehabilitation robot based on the Euler-Lagrange equation;

[0009] Step 2: Design a fractional-order terminal sliding surface for the lower limb exoskeleton rehabilitation robot system to meet its complex control requirements;

[0010] Step 3: Based on the lower limb exoskeleton rehabilitation robot dynamics model established in step 1 and the sliding surface designed in step 2, design the equivalent control law and the switching control law;

[0011] Step 4: Based on Lyapunov stability theory, prove that the control law designed in step 3 can make the system reach a stable state, and perform motion performance analysis and simulation verification on the designed fractional-order terminal sliding mode control algorithm on the MATLAB / Simulink software platform.

[0012] The second aspect of the present invention relates to a fractional-order terminal sliding mode control device applied to a lower limb rehabilitation robot, comprising a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement a fractional-order terminal sliding mode control method applied to a lower limb rehabilitation robot of the present invention.

[0013] A third aspect of the present invention relates to a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements a fractional-order terminal sliding mode control method for a lower limb rehabilitation robot of the present invention.

[0014] The present invention takes into account the parameter uncertainty of dynamic modeling, and provides a fractional-order terminal sliding mode control method, which can better adapt to system changes and external disturbances, and enhance the robustness of the control system. Compared with the existing control methods, the beneficial effects of the present invention are embodied in: the present invention takes into account the trajectory tracking control of the lower limb exoskeleton rehabilitation robot under the condition of dynamic modeling parameter uncertainty, and provides a fractional-order terminal sliding mode control method, which enhances the robustness of the control system. The fractional-order terminal sliding mode control law is designed to better cope with the parameter perturbation, strong time-varying and nonlinear characteristics of the system. Finally, the present invention verifies through simulation that this fractional-order terminal sliding mode control method can significantly improve the motion stability and trajectory tracking accuracy of the lower limb exoskeleton rehabilitation robot, and meet the application needs of hemiplegic patients during rehabilitation training. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the technical solution of the present invention, the following is a brief description of the drawings mentioned in the technical description of the present invention. Obviously, the drawings described below are only schematic diagrams of some embodiments of the present invention. For those skilled in the art, other similar diagrams can be obtained based on these drawings without creative work.

[0016] Figure 1 It is a structural diagram of the dynamic model of the lower limb exoskeleton rehabilitation robot of the present invention;

[0017] Figure 2 It is a MATLAB / Simulink software platform simulation program diagram of the present invention;

[0018] Figure 3 This is the tracking effect diagram of hip joint motion trajectory simulated and tested on MATLAB / Simulink software platform;

[0019] Figure 4 This is the tracking effect diagram of the knee joint motion trajectory simulated and tested on the MATLAB / Simulink software platform;

[0020] Figure 5 The following are the tracking error diagrams of the hip and knee joints simulated and tested on the MATLAB / Simulink software platform;

[0021] Figure 6 The output torque diagram of the hip and knee joint motors simulated and tested on the MATLAB / Simulink software platform;

[0022] Figure 7 The figure is a flow chart of the method of the present invention. DETAILED DESCRIPTION

[0023] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0024] Example 1

[0025] This embodiment relates to a fractional-order terminal sliding mode control method applied to a lower limb rehabilitation robot, and the specific implementation steps are as follows:

[0026] Step 1: Establish a plane rectangular coordinate system under the sagittal plane, and establish a dynamic model of the lower limb exoskeleton rehabilitation robot based on the Euler-Lagrange equation;

[0027] like Figure 1 As shown in the figure, a rectangular coordinate system is established on the sagittal plane of the human body, and the movement of the lower limbs of the human body in three-dimensional space is regarded as a plane movement on the sagittal plane. Considering that the ankle joint has little effect on the movement of the human body, in the dynamic model of the lower limb exoskeleton rehabilitation robot, the hip joint and knee joint are regarded as active joints, and the ankle joint is regarded as a passive joint. Let O1(x1,y1) and O2(x2,y2) be the centroid coordinates of the thigh segment and the calf segment respectively, then the centroid coordinates can be expressed as follows:

[0028]

[0029] Among them, l1 and l2 are the lengths of the thigh and calf segments respectively; l c1 and l c2 They represent the distance from the hip joint to the center of mass of the thigh and from the knee joint to the center of mass of the calf respectively; q1 and q2 are the position coordinates of the hip joint and the knee joint respectively, and it is stipulated that the counterclockwise rotation of the joint around the axis perpendicular to the sagittal plane is the positive direction.

[0030] Next, the Lagrangian function of the dynamic system is defined in the generalized coordinate system as:

[0031] L=E k -E p (2)

[0032] Among them, L, E k and E p They represent the total mechanical energy, kinetic energy and potential energy of the system respectively.

[0033] The Lagrange equation of the system is expressed as:

[0034]

[0035] Where q = [q1 q2] T is the joint angle; τ=[τ1τ2] Tis the control signal, i.e. the output torque of the joint motor. The total kinetic energy and total potential energy of the system can be calculated as:

[0036]

[0037] Among them, m1 and m2 are the masses of the thigh segment and the calf segment respectively; I1 and I2 represent the moment of inertia of the thigh segment and the calf segment respectively.

[0038] The dynamic equation of the lower limb exoskeleton rehabilitation robot can be solved by combining equations (2), (3) and (4):

[0039]

[0040] Taking into account the existence of system model parameter perturbations and external disturbances, the overall model of the lower limb exoskeleton rehabilitation robot can be expressed as:

[0041]

[0042] Among them, M represents the inertia matrix, C represents the Coriolis force and centrifugal force matrix, G represents the gravity torque vector; ΔM, ΔC and ΔG represent the parameter uncertainty of the system; parameters τ and d represent the joint motor output torque and external disturbance torque of the system respectively. For the convenience of description, a disturbance function f(t) is used to replace the unmodeled disturbance and external disturbance of the controlled object, which is given by the following formula:

[0043]

[0044] Finally, the dynamic model of the lower limb exoskeleton rehabilitation robot can be expressed as follows:

[0045]

[0046] in,

[0047]

[0048]

[0049] Step 2: Design a fractional-order terminal sliding surface for the lower limb exoskeleton rehabilitation robot system to meet its complex control requirements;

[0050] Before designing the sliding surface, we need to introduce some basic knowledge of fractional calculus. The c-order Riemann-Liouville fractional derivative and integral of the function f(t) on the interval [t0, t] are defined as follows:

[0051]

[0052] Where n-1<c≤n,n∈N; Γ(·) is the Gamma function, which is defined as follows:

[0053]

[0054] In the lower limb exoskeleton rehabilitation robot system, the interference generated by the external environment is often constrained by the physical system itself. Therefore, assuming that the parameter uncertainty and system interference of the dynamic model established in step 1 are bounded, the tracking error is defined as:

[0055]

[0056] Among them, q r1 and q r2 are the gait reference trajectories of the hip joint and knee joint respectively. Then the designed fractional-order terminal sliding surface is as follows:

[0057]

[0058] Where s = [s1 s2] T ; k1 = diag(k 11 ,k 12 ) and k2=diag(k 21 ,k 22 ) are all positive definite coefficient matrices; the fractional error vector I α sig ρ (e) and D β sig σ (e) Satisfaction The function sig x (·) is a smooth signed power function defined as sig x (·)=|·| x sgn(·); sliding surface index parameter satisfies 0<α i ,β i ,ρ i ,σ i <1,i=1,2.

[0059] Step 3: Based on the lower limb exoskeleton rehabilitation robot dynamics model established in step 1 and the sliding surface designed in step 2, design the equivalent control law and the switching control law;

[0060] According to formula (16), the first-order derivative of the sliding surface is obtained:

[0061]

[0062] From formula (9), a variation of the dynamic model of the lower limb exoskeleton rehabilitation robot can be obtained:

[0063]

[0064] Combined with equation (14), let We can get:

[0065]

[0066] The equivalent control law can be solved and defined as τ eq , as shown below:

[0067]

[0068] In order to attract the system state to the sliding surface and maintain its motion on the sliding surface, a typical power reaching law is selected as follows:

[0069]

[0070] Among them, the coefficient matrix k3=diag(k 31 ,k 32 ), like k1 and k2, they are all positive definite matrices and satisfy k ij >0; satisfy

[0071] Based on equations (19) and (20), the total control signal of the system can be obtained as:

[0072]

[0073] Step 4: Based on Lyapunov stability theory, prove that the control law designed in step 3 can make the system reach a stable state, and perform motion performance analysis and simulation verification of the designed sliding mode control algorithm on the MATLAB / Simulink software platform.

[0074] Define the Lyapunov function:

[0075]

[0076] Taking the first-order derivative of equation (22), we can obtain:

[0077]

[0078] Substituting equation (14) and equation (16) into equation (23), we can obtain:

[0079]

[0080] Furthermore, by combining equation (17) and equation (21), we can obtain:

[0081]

[0082] Among them, M, k3 are both positive definite matrices, is a power term greater than zero. Therefore, when s≠0, we can get V s <0. In addition, when s≡0, there must be This shows that the state of the system can be moved to the designed sliding surface, and under a given control signal, the system is asymptotically stable.

[0083] In order to reduce the jitter effect caused by the sign function, the saturation function is used instead of the sign function. The improved control signal is:

[0084]

[0085] in,

[0086]

[0087] Finally, the simulation analysis is performed using the MATLAB / Simulink simulation platform with software version 2022a. All simulations are performed using the ode4 solver of the MATLAB software, with a simulation time of 30 seconds and a fixed sampling step of 0.001 seconds. In order to verify the robustness of the designed fractional-order terminal sliding mode controller, the system modeling error and external disturbance are set to f = [10sin(t)10sin(t)] T The parameters of the dynamic model of the given lower limb exoskeleton rehabilitation robot are as follows:

[0088] name symbol Numeric Thigh mass <![CDATA[m1]]> 6.099kg Thigh segment moment of inertia <![CDATA[I1]]> <![CDATA[0.084kg·m 2 ]]> Thigh length <![CDATA[l1]]> 0.460m Distance from hip joint to thigh center of gravity <![CDATA[l c1 ]]> 0.405m Calf quality <![CDATA[m2]]> 4.257kg Lower leg moment of inertia <![CDATA[I2]]> <![CDATA[0.569kg·m 2 ]]> Calf length <![CDATA[l2]]> 0.480m The distance between the knee joint and the center of gravity of the calf segment <![CDATA[l c2 ]]> 0.228m Gravity acceleration g <![CDATA[9.79m·s 2 ]]>

[0089] In the simulation, the reference gait trajectory of the given lower limb exoskeleton rehabilitation robot is shown below:

[0090]

[0091] Among them, ω1=3.884,ω2=3.863,T p =δt, δ is used to adjust the reference gait cycle, and δ=1 in this simulation. The simulation program built on the MATLAB / Simulink software platform is as follows Figure 2 The simulation results are shown in Figure 3 , Figure 4 , Figure 5 and Figure 6 shown.

[0092] The simulation results show that in the presence of external disturbances, the designed fractional-order terminal sliding mode control algorithm can enable the lower limb exoskeleton rehabilitation robot to achieve stable gait trajectory tracking. After reaching a stable state, the tracking errors of the hip and knee joints can be limited to a very small range of about ±0.004rad, which meets the tracking control requirements. The output torque of the joint motor ranges from -25 to 20N·m, and is relatively smooth without obvious high-frequency jitter, indicating that the designed fractional-order terminal sliding mode control algorithm has good control effect and robustness.

[0093] Example 2

[0094] The present embodiment relates to a fractional-order terminal sliding mode control device applied to a lower limb rehabilitation robot, comprising a memory and one or more processors, wherein the memory stores executable code, and when the one or more processors execute the executable code, they are used to implement a fractional-order terminal sliding mode control method applied to a lower limb rehabilitation robot of the present invention.

[0095] Example 3

[0096] The present embodiment relates to a computer-readable storage medium having a program stored thereon. When the program is executed by a processor, a fractional-order terminal sliding mode control method for a lower limb rehabilitation robot of the present invention is implemented.

[0097] The above content only represents one embodiment of the present invention and does not limit the scope of application of the present invention. In the opinion of professionals in the relevant technical field, the present invention can be modified and altered in many different ways. Any adjustment, substitution or improvement made within the scope of the core concept and principle of the present invention should be regarded as part of the protection scope of the present invention.

Claims

1. A fractional-order terminal sliding mode control method for a lower limb rehabilitation robot, comprising the following steps: Step 1: Establish a plane rectangular coordinate system under the sagittal plane, and establish a dynamic model of the lower limb exoskeleton rehabilitation robot based on the Euler-Lagrange equation; Step 2: Design a fractional-order terminal sliding surface for the lower limb exoskeleton rehabilitation robot system to meet its complex control requirements; Step 3: Based on the lower limb exoskeleton rehabilitation robot dynamics model established in step 1 and the sliding surface designed in step 2, design the equivalent control law and the switching control law; Step 4: Based on Lyapunov stability theory, prove that the control law designed in step 3 can make the system reach a stable state, and perform motion performance analysis and simulation verification on the designed fractional-order terminal sliding mode control algorithm on the MATLAB / Simulink software platform.

2. A fractional-order terminal sliding mode control method for a lower limb rehabilitation robot, characterized in that: Step 1 specifically includes: establishing a plane rectangular coordinate system on the sagittal plane of the human body, and treating the movement of the lower limbs of the human body in three-dimensional space as planar movement on the sagittal plane. Considering that the ankle joint has little effect on the movement of the human body, in the dynamic model of the lower limb exoskeleton rehabilitation robot, the hip joint and knee joint are regarded as active joints, and the ankle joint is regarded as a passive joint. Let O1(x1,y1) and O2(x2,y2) be the center of mass coordinates of the thigh segment and the calf segment respectively, then the center of mass coordinates can be expressed as follows: Among them, l1 and l2 are the lengths of the thigh and calf segments respectively; l c1 and l c2 They represent the distance from the hip joint to the center of mass of the thigh and from the knee joint to the center of mass of the calf respectively; q1 and q2 are the position coordinates of the hip joint and the knee joint respectively, and it is stipulated that the counterclockwise rotation of the joint around the axis perpendicular to the sagittal plane is the positive direction. Next, the Lagrangian function of the dynamic system is defined in the generalized coordinate system as: L=E k -AND p (2) Among them, L, E k and E p They represent the total mechanical energy, kinetic energy and potential energy of the system respectively. The Lagrange equation of the system is expressed as: Where q = [q1 q2] T is the joint angle; τ=[τ1τ2] T is the control signal, i.e. the output torque of the joint motor. The total kinetic energy and total potential energy of the system can be calculated as: Among them, m1 and m2 are the masses of the thigh segment and the calf segment respectively; I1 and I2 represent the moment of inertia of the thigh segment and the calf segment respectively. The dynamic equation of the lower limb exoskeleton rehabilitation robot can be solved by combining equations (2), (3) and (4): Taking into account the existence of system model parameter perturbations and external disturbances, the overall model of the lower limb exoskeleton rehabilitation robot can be expressed as: Among them, M represents the inertia matrix, C represents the Coriolis force and centrifugal force matrix, G represents the gravity torque vector; ΔM, ΔC and ΔG represent the parameter uncertainty of the system; parameters τ and d represent the joint motor output torque and external disturbance torque of the system respectively. For the convenience of description, a disturbance function f(t) is used to replace the unmodeled disturbance and external disturbance of the controlled object, which is given by the following formula: Finally, the dynamic model of the lower limb exoskeleton rehabilitation robot can be expressed as follows: in, 3. A fractional-order terminal sliding mode control method for a lower limb rehabilitation robot, characterized in that: Step 2 specifically includes: The c-order Riemann-Liouville fractional derivative and integral of the function f(t) on the interval [t0,t] are defined as follows: Where n-1<c≤n,n∈N; Γ(·) is the Gamma function, which is defined as follows: In the lower limb exoskeleton rehabilitation robot system, the interference generated by the external environment is often constrained by the physical system itself. Assuming that the parameter uncertainty and system interference of the dynamic model established in step 1 are bounded, the tracking error is defined as: Among them, q r1 and q r2 are the gait reference trajectories of the hip joint and knee joint respectively. The designed fractional-order terminal sliding surface is as follows: Where s = [s1 s2] T ; k1 = diag(k 11 ,k 12 ) and k2=diag(k 21 ,k 22 ) are all positive definite coefficient matrices; the fractional error vector I α sig ρ (e) and D β sig σ (e) Satisfaction The function sig x (·) is a smooth signed power function defined as sig x (·)=|·| x sgn(·); sliding surface index parameter satisfies 0<α i ,β i ,ρ i ,σ i <1,i=1,2.

4. A fractional-order terminal sliding mode control method for a lower limb rehabilitation robot, characterized in that: Step 3 specifically includes: According to formula (16), the first-order derivative of the sliding surface is obtained: From formula (9), a variation of the dynamic model of the lower limb exoskeleton rehabilitation robot can be obtained: Combined with equation (14), let We can get: The equivalent control law can be solved and defined as τ eq , as shown below: In order to attract the system state to the sliding surface and maintain its motion on the sliding surface, a typical power reaching law is selected as follows: Among them, the coefficient matrix k3=diag(k 31 ,k 32 ), like k1 and k2, they are all positive definite matrices and satisfy k ij >0; satisfy Based on equations (19) and (20), the total control signal of the system can be obtained as:

5. A fractional-order terminal sliding mode control method for a lower limb rehabilitation robot, characterized in that: Step 4 specifically includes: Define the Lyapunov function: Taking the first-order derivative of equation (22), we can obtain: Substituting equation (14) and equation (16) into equation (23), we can obtain: Furthermore, by combining equation (17) and equation (21), we can obtain: Among them, M, k3 are both positive definite matrices, is a power term greater than zero. Therefore, when s≠0, we can get V s <0. In addition, when s≡0, there must be This shows that the state of the system can be moved to the designed sliding surface, and under a given control signal, the system is asymptotically stable. In order to reduce the jitter effect caused by the sign function, the saturation function is used instead of the sign function. The improved control signal is: in, 6. A fractional order terminal sliding mode control device applied to a lower limb rehabilitation robot, characterized in that: It comprises a memory and one or more processors, wherein the memory stores executable codes, and when the one or more processors execute the executable codes, they are used to implement a fractional-order terminal sliding mode control method for a lower limb rehabilitation robot as described in any one of claims 1 to 5.

7. A computer-readable storage medium, characterized in that: A program is stored thereon, and when the program is executed by a processor, a fractional-order terminal sliding mode control method for a lower limb rehabilitation robot according to any one of claims 1 to 5 is implemented.

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