Rehabilitation robot adaptive fractional order sliding mode control method based on disturbance observer

Abstract

The invention discloses a self-adaptive fractional order sliding mode control method for a rehabilitation robot based on a disturbance observer. The method mainly comprises the following steps: firstly, carrying out dynamic modeling on the rehabilitation robot based on the Lagrange method; secondly, the observable interference in a rehabilitation robot control system is inhibited through a control method for constructing an interference observer, and the robustness and the anti-interference capability of a controller are improved; secondly, designing a fractional order sliding mode controller based on a fractional order calculus theory, improving the dynamic performance of a control system and reducing buffeting; furthermore, the index sliding mode approaching rate is designed, the adjusting time of the control system is shortened, the chattering phenomenon of the control system is weakened, and the dynamic quality of the control system is further improved; and finally, estimating and compensating the unobservable part of the interference through adaptive law control, and improving the adaptability of the control system to parameter uncertainty and external interference. The method can effectively improve the trajectory tracking precision and anti-interference capability of the rehabilitation robot, and is suitable for accurate motion control in the rehabilitation training process.

Description

Technical Field

[0001] This invention belongs to the field of robot control technology, and more specifically, relates to a control method for a rehabilitation robot to stably track a reference trajectory. Background Technology

[0002] Rehabilitation robots, as important medical devices in the field of rehabilitation, can provide patients with precise and repeatable rehabilitation training, playing an increasingly important role, especially in the rehabilitation treatment of patients with neurological diseases such as stroke and spinal cord injury. To simulate human joint movements, rehabilitation robots typically employ a multi-degree-of-freedom serial robotic arm structure to assist patients in their training.

[0003] However, rehabilitation robots face many challenges in practical applications: (i) Rehabilitation robots need to come into direct contact with the human body during operation. The human body is a highly time-varying nonlinear system, which brings great uncertainty to the robot control system; (ii) The structural complexity of the rehabilitation robot itself, the uncertainty of model parameters, and external interference all put forward higher requirements for the accuracy and stability of the control system; (iii) The rehabilitation robot system is a nonlinear, strongly coupled multi-input output system, so the design of the controller also faces great challenges.

[0004] Currently, the main control methods for robotic arms include PID control, fuzzy control, neural network control, and sliding mode control. Among these, sliding mode control is widely used in robotic arm control because it is insensitive to external disturbances. However, low-order sliding mode control suffers from chattering in practical applications, which reduces the control accuracy and stability of the system and affects the service life of the robotic arm joints.

[0005] In recent years, fractional calculus theory has made significant progress in the application of control. Compared with integer calculus, fractional derivatives have the advantage of remembering previous values ​​and possessing a larger stability region with more open parameters, thus enhancing controller performance. Combining fractional calculus theory with sliding mode control has formed fractional sliding mode control, which can effectively improve the dynamic and steady-state performance of control systems.

[0006] Furthermore, as an effective method for disturbance estimation and compensation, the disturbance observer can estimate disturbances in the system in real time and compensate for the disturbances in the controller, thereby improving the anti-interference capability of the control system.

[0007] Therefore, designing a high-precision and robust control method for rehabilitation robots by combining fractional calculus theory and disturbance observation techniques is an important research topic. This invention proposes an adaptive fractional sliding mode control method based on a disturbance observer. It utilizes a disturbance observer to estimate and compensate for observable disturbances to the robotic arm, designs a fractional sliding surface to improve the response speed of trajectory tracking, and designs an adaptive law to improve the tracking accuracy of the controller and reduce system jitter. This control method effectively improves the trajectory tracking accuracy of the robotic arm and greatly promotes the realization of precise control of the robotic arm. Summary of the Invention

[0008] To address the problems encountered in synovial control in the prior art, this invention proposes an adaptive fractional-order synovial control method for rehabilitation robots based on a disturbance observer, specifically addressing the insufficient tracking accuracy and robustness in motion control. This control method overcomes the influence of model parameter uncertainties and multi-source disturbances (friction between joints within the robotic arm, and external uncertainties) on precise motion control during robot movement. Simultaneously, it ensures stable system control, reduces tracking errors, lowers system jitter, and improves the dynamic performance of the control system.

[0009] The technical solution of this invention: An adaptive fractional-order synovial control method for a rehabilitation robot based on an interference observer, comprising the following steps:

[0010] Step 1: The rehabilitation robot of this invention adopts a six-degree-of-freedom robotic arm. Considering the uncertainty, nonlinearity, and external disturbances of the model parameters of the six-degree-of-freedom rehabilitation robot, the dynamic state equation of the six-degree-of-freedom rehabilitation robot is established using the Lagrange method;

[0011] Step 2: Design of the control system disturbance observer. Based on the dynamic state equation of the six-degree-of-freedom rehabilitation robot, a disturbance observer is constructed to estimate and compensate for observable disturbances in the control system in real time.

[0012] Step 3: Design of fractional-order sliding mode controller to achieve precise trajectory tracking control of the six-degree-of-freedom rehabilitation robot;

[0013] Step 4: Sliding diaphragm approach rate design to shorten the adjustment time of the control system, accelerate the convergence speed of the control system, and reduce the chattering phenomenon of the control system.

[0014] Step 5: Design the adaptive law of the control system to estimate and compensate for the unobservable part of the disturbance;

[0015] Step Six: Apply the designed control method to the control system of the six-degree-of-freedom rehabilitation robot to achieve precise tracking control of its trajectory.

[0016] The above solution addresses the issues of insufficient tracking accuracy and robustness in the trajectory tracking process of a six-degree-of-freedom rehabilitation robot, and also reduces the jitter phenomenon in the control system.

[0017] This method has the following advantages:

[0018] (1) This invention introduces a disturbance observer, which performs real-time observation of the observable disturbance in the control system. By designing and adjusting the gain matrix of the disturbance observer, the observable error of the control system can be exponentially reduced and eventually converged. Using a disturbance observer can greatly reduce the impact of disturbances on the control system, thereby improving the tracking accuracy of the control system.

[0019] (2) Based on existing sliding diaphragm control methods, this invention incorporates the principle of fractional calculus to design a fractional sliding diaphragm control surface, ensuring good robustness of the control system. Furthermore, this invention employs an exponential reaching law, which effectively improves chattering in the control system while significantly reducing convergence time and tracking error.

[0020] (3) In the selection of the adaptive law, this invention designs a Lyapunov function and combines it with a fractional sliding diaphragm controller and the designed control law, selects reasonable parameters, and designs a suitable adaptive law, so as to ensure that the control system can meet the Lyapunov stability theory while improving the tracking accuracy and dynamic performance of the control system.

[0021] (4) The present invention can flexibly optimize the dynamic and steady-state performance of the control system by adjusting the order of the fractional differential operator, so that the rehabilitation robot can adapt to different motion control needs. Attached Figure Description

[0022] Figure 1 Modeling an improved DH method for robotic arms;

[0023] Figure 2 This is a structural block diagram of the control system of the method of the present invention;

[0024] Figure 3 This is the angular displacement tracking curve of the robotic arm tracking the reference trajectory of the present invention;

[0025] Figure 4 This is the angular velocity tracking curve of the robotic arm tracking the reference trajectory of the present invention;

[0026] Figure 5 This is the angular displacement error curve of the robotic arm tracking the reference trajectory of the present invention;

[0027] Figure 6 This is the curve showing the change in control torque of the robotic arm tracking the reference trajectory in this invention. Detailed Implementation

[0028] To address the issues of insufficient tracking accuracy, robustness, and control system jitter encountered in sliding diaphragm control, this invention proposes an adaptive fractional-order sliding diaphragm control method for rehabilitation robots based on a disturbance observer. This method improves the tracking accuracy and robustness of the control system, enhances its dynamic performance, and reduces its jitter while ensuring stable operation. The invention is described in detail below with reference to the accompanying drawings and specific implementation examples.

[0029] Reference Figure 1 and reference Figure 2 The present invention will be further described as follows:

[0030] This invention proposes an adaptive fractional-order synovial control method for rehabilitation robots based on an interference observer, the specific steps of which include the following:

[0031] Step 1: The rehabilitation robot of this invention adopts a six-degree-of-freedom robotic arm. Considering the uncertainty, nonlinearity, and external disturbances of the model parameters of the six-degree-of-freedom rehabilitation robot, the dynamic state equation of the six-degree-of-freedom rehabilitation robot is established using the Lagrange method.

[0032] Step one specifically involves establishing the dynamic state equations of the six-degree-of-freedom rehabilitation robot as follows.

[0033] Define the Lagrange function as:

[0034]

[0035] In the formula: L is the Lagrangian function, K is the total kinetic energy of the robotic arm system, and P is the total potential energy of the robotic arm system.

[0036] in,

[0037]

[0038]

[0039]

[0040]

[0041] In the formula: q = [q1, q2, ..., q6] represents the joint angles of each joint of the robotic arm in the generalized coordinate system; T is the homogeneous rotation matrix; J i The matrix is ​​a pseudo-inertia matrix; m iLet J be the mass of link i; x̅, y̅, z̅ be the expressions for the center of mass of link i in the coordinate system; J is the mass of link i. ixx J iyy J izz Let g̅ be the product of inertia of the link; g̅ = [g, 0] T The expression for the gravitational acceleration vector; This is the expression for the center of mass of link i in the coordinate system.

[0042] Based on the Lagrange method modeling of robotic arm dynamics, the following equations can be obtained:

[0043]

[0044] Combining equations (1) to (6), the dynamic equation of the robotic arm can be obtained as follows:

[0045]

[0046]

[0047]

[0048]

[0049] In the formula: τ ∈ R n × 1 q is the control torque of the robotic arm; M(q) is the inertia matrix of the robotic arm; C(q, q̇) is the centrifugal force and Coriolis force matrix of the robotic arm; G(q) is the gravity term matrix of the robotic arm.

[0050] Due to the inherent uncertainty disturbance δ and the difficulty in identifying dynamic parameters, it is challenging to establish an accurate dynamic model for the robotic arm. Therefore, based on the theoretical dynamic model of the robotic arm, a nominal model of its dynamic equations is constructed. The dynamic equations are as follows:

[0051]

[0052]

[0053] In the formula: M(q) = M0(q) + ΔM(q), C(q, q̇) = C0(q, q̇) + ΔC(q, q̇), G(q) = G0(q) + ΔG(q); M0(q), C0(q, q̇), and G0(q) are the parameters in the nominal model of the robotic arm; ΔM(q), ΔC(q, q̇), and ΔG(q) are the uncertain terms in the dynamic model, which are the model errors of the robotic arm system.

[0054] Step 2: Design a system disturbance observer. Based on the dynamic state equation of the six-degree-of-freedom rehabilitation robot, construct a disturbance observer to estimate and compensate for observable disturbances in the control system in real time.

[0055] Step two specifically involves the following design process for the interference observer.

[0056] First, from formula (11), the composite disturbance of the robotic arm can be obtained as follows:

[0057]

[0058] The estimated value of the disturbance f is defined as follows: The estimation error of the composite disturbance is defined as:

[0059]

[0060] Secondly, the interference observer is defined as follows:

[0061]

[0062] In the formula: L(q, q̇) is the design gain of the interference observer.

[0063] Finally, assuming the perturbation changes slowly with respect to the perturbation observer, i.e., ḟ = 0, we can deduce that:

[0064]

[0065] By designing an appropriate gain for the interference observer, the observation error can be made to converge exponentially.

[0066] However, it is difficult to obtain the acceleration of each joint during the actual movement of the robotic arm, therefore, the following definition is given:

[0067]

[0068] In the formula: z is a defined auxiliary variable; p(q, q̇) is a defined nonlinear function.

[0069] From equations (13) to (17), the designed interference observer is:

[0070]

[0071] Therefore, after adopting the disturbance observer, the composite disturbance was reduced from f to F. The dynamic equation of the robotic arm based on the disturbance observer is:

[0072]

[0073] Steps 3 and 4: Design a fractional-order sliding mode controller to achieve precise trajectory tracking control of the six-degree-of-freedom rehabilitation robot; design a sliding mode approach rate to shorten the adjustment time of the control system, accelerate the convergence speed of the control system, and reduce the chattering phenomenon of the control system.

[0074] Steps three and four are specifically as follows: The fractional-order synovial controller and the synovial convergence rate are designed as follows.

[0075] Define the robotic arm trajectory tracking error as:

[0076]

[0077] In the formula: q d ,q̇ d ,q̈ d These are the angular displacement, angular velocity, and angular acceleration of the reference trajectory, respectively.

[0078] To improve the transient performance of the sliding diaphragm control and suppress jitter, a fractional-order sliding diaphragm control law is designed as follows:

[0079]

[0080] Among them, μ∈(1,2), λ∈(1,2), α = diag(α1, α2, ···, α n ) > 0, β = diag(β1,β2, ···, β n ) > 0 are all parameters to be designed; sign represents the sign function; D u-1 e is the fractional derivative of the error e.

[0081] The fractional operators are defined as follows:

[0082]

[0083] The dynamic equations of the robotic arm based on the interference observer established by equation (19) are as follows:

[0084]

[0085] Based on equations (21) to (23), we can obtain:

[0086]

[0087] The sliding contact rate of the control system is the exponential rate of convergence.

[0088]

[0089] Therefore, based on equations (24) and (25), the system control law is designed as: τ = τ eq + τ u + τ f .

[0090] Equivalent control law τ eq for:

[0091]

[0092] Robust control law τ u for:

[0093]

[0094] Disturbance suppression control law τ f for:

[0095]

[0096] Where v represents the item to be designed.

[0097] Step 5: Design an adaptive law for the control system to estimate and compensate for the unobservable part of the disturbance.

[0098] Step five specifically involves designing the adaptive law for the control system as follows.

[0099] For equations (24) to (28), we have:

[0100]

[0101] Let the uncertainty disturbance Γ = -M0(q) －1 F, The estimated value is given, and the deviation between the actual value and the estimated value is defined as follows: .

[0102] Therefore, in order to obtain the estimated uncertainty perturbation, the Lyapunov function is defined as:

[0103]

[0104] In the formula: All elements are positive.

[0105] Differentiating the Lyapunov function, we get:

[0106]

[0107] Based on Lyapunov's second stability theorem, design an adaptive law for the control system: , ,have:

[0108]

[0109] According to Lyapunov's second stability theorem, the selected Lyapunov function satisfies V ≥ 0 and V̇ ≤ 0, therefore the closed-loop control system is asymptotically stable.

[0110] To reduce the jitter effect associated with the sign function, the parameter k1, representing the uncertainty limit, can be selected using the following adaptive estimate:

[0111]

[0112] Where η is a positive parameter.

[0113] In order to further suppress the jitter caused by the sign function sign(s) in the synovial control law, the switching function in the control law is replaced by a smooth hyperbolic function tanh(s).

[0114] In summary, the control law of the robotic arm system is:

[0115]

[0116] Step Six: Apply the designed control method to the six-degree-of-freedom rehabilitation robot system to achieve precise trajectory tracking control.

[0117] Finally, to verify the feasibility and effectiveness of the proposed method, MATLAB and SIMULINK were used as simulation experimental platforms, along with the built-in Robotics System Toolbox and SimMechanics plugin. A six-DOF robotic arm was used as the experimental object in the simulation experiment, and the simulation parameters were set as follows:

[0118] Robotic arm reference trajectory selection:

[0119]

[0120] Parameter settings: .

[0121] Perturbation settings: Modeling errors ΔM(q) = 0.1M(q), ΔC(q, q̇) = 0.1C(q, q̇), ΔG(q) = 0.1G(q); Joint friction is the sum of Coulomb friction and viscous friction F(q̇) = 1.5sign(q̇) + 0.5q̇; Other perturbations are sinusoidal signals with small amplitudes τ. d = 3sin(πt).

[0122] The simulation results of the adaptive fractional-order synovial control method for rehabilitation robots based on disturbance observers proposed in this invention are as follows: Figures 3 to 6 As shown. Figure 3 This demonstrates the changes in joint angle tracking reference trajectory during the movement of the robotic arm. Figure 4 The simulation demonstrates the change in the angular velocity of the robotic arm as it tracks the reference trajectory. The simulation results verify the correctness of the theory, showing that the joint angles can converge quickly and accurately track the desired trajectory even under model uncertainties and unknown disturbances.

[0123] Figure 5 This demonstrates the tracking error of the robotic arm's joint angles, further showcasing the accuracy of trajectory tracking. For example... Figure 6 As shown in the figure, the control torque curve is continuous and smooth, which greatly reduces chattering in sliding mode control. Table 1 shows the tracking error of the joint angles of the robotic arm based on this control method.

[0124] Table 1 Tracking error of each joint angle of the robotic arm

[0125] joint Convergence time / s (error < 0.05 rad) Maximum steady-state error / rad Average steady-state error / rad Mean square error / rad Joint 1 0.41715 0.027448 -0.0077228 0.011036 Joint 2 0.44795 0.042847 -0.0075338 0.013062 Joint 3 0.41715 0.039805 -0.0073818 0.013050 Joint 4 0.42573 0.026963 -0.0075545 0.010077 Joint 5 0.4343 0.028014 -0.0083247 0.010499 Joint 6 0.41715 0.035634 -0.0075754 0.012396

[0126] The experimental results above demonstrate that the adaptive fractional-order synovial control method for rehabilitation robots based on disturbance observers, as designed in this invention, exhibits excellent transient performance and disturbance resistance. It demonstrates strong robustness in the presence of multi-source disturbances and effectively overcomes the influence of model parameter uncertainties. This control system ensures stable control while reducing joint angle tracking errors in multiple robotic arms, thus improving overall control performance. Particularly during rehabilitation training, it adapts to the uncertainties in the interaction between the human body and the robot, providing precise and stable motion control to meet the high-precision requirements of rehabilitation training.

[0127] The foregoing description provides a detailed account of embodiments of the present invention and is not intended to limit the invention in any way. Those skilled in the art can make various optimizations, improvements, and modifications based on this invention. Therefore, the scope of protection of this invention should be defined by the appended claims.

Claims

1. An adaptive fractional-order sliding membrane control method for a rehabilitation robot based on a disturbance observer, characterized in that: The method includes the following steps: S1: The rehabilitation robot adopts a six-degree-of-freedom robotic arm; considering the uncertainty, nonlinearity and external disturbance of the model parameters of the six-degree-of-freedom rehabilitation robot, the dynamic state equation of the six-degree-of-freedom rehabilitation robot is established by using the Lagrange method; S2: System disturbance observer design. Based on the dynamic state equation of the six-degree-of-freedom rehabilitation robot, a disturbance observer is constructed to estimate and compensate for observable disturbances in the control system in real time. S3: Fractional-order sliding mode controller design to achieve precise trajectory tracking control of a six-degree-of-freedom rehabilitation robot; S4: Sliding diaphragm approach rate design shortens the adjustment time of the control system, accelerates the convergence speed of the control system, and reduces the chattering phenomenon of the control system. S5: Adaptive law design for control systems, which estimates and compensates for the unobservable parts of disturbances; S6: The designed control method is applied to the control system of a six-degree-of-freedom rehabilitation robot to achieve precise tracking control of its trajectory.

2. The adaptive fractional-order sliding membrane control method for a rehabilitation robot based on an interference observer according to claim 1, characterized in that, The dynamic state equations of the six-degree-of-freedom rehabilitation robot are established as follows: Define the Lagrange function: In the formula: L is the Lagrangian function, K is the total kinetic energy of the robotic arm system, and P is the total potential energy of the robotic arm system; where, In the formula: q = [q1, q2, ..., q6] represents the joint angles of each joint of the robotic arm in the generalized coordinate system; T is the homogeneous rotation matrix; J i The matrix is ​​a pseudo-inertia matrix; m i Let J be the mass of link i; x̅, y̅, z̅ be the expressions for the center of mass of link i in the coordinate system; J is the mass of link i. ixx J iyy J izz Let g̅ be the product of inertia of the link; g̅ = [g, 0] T The expression for the gravitational acceleration vector; This is the expression for the centroid of link i in the coordinate system; Based on the Lagrange method modeling of robotic arm dynamics, the following equations are obtained: Combining equations (1) to (6), the dynamic equation of the robotic arm can be obtained as follows: In the formula: τ ∈ R n × 1 Let M(q) be the control torque of the robotic arm; M(q) be the inertia matrix of the robotic arm; C(q, q̇) be the centrifugal force and Coriolis force matrix of the robotic arm; and G(q) be the gravity term matrix of the robotic arm. Based on the theoretical dynamic model of the robotic arm, a nominal model of the robotic arm's dynamic equations is constructed; its dynamic equations are: In the formula: M(q) = M0(q) + ΔM(q), C(q, q̇) = C0(q, q̇) + ΔC(q, q̇), G(q) = G0(q) + ΔG(q); M0(q), C0(q, q̇), and G0(q) are the parameters in the nominal model of the robotic arm; ΔM(q), ΔC(q, q̇), and ΔG(q) are the uncertain terms in the dynamic model, which are the model errors of the robotic arm system.

3. The adaptive fractional-order sliding membrane control method for a rehabilitation robot based on an interference observer according to claim 2, characterized in that, The design process for the interference observer is as follows: First, from equation (11), the composite disturbance of the robotic arm can be obtained as follows: The estimated value of the disturbance f is defined as follows: The estimation error of the composite disturbance is defined as: Secondly, the interference observer is defined as follows: In the formula: L(q, q̇) is the design gain of the interference observer; Finally, assuming the perturbation changes slowly with respect to the perturbation observer, i.e., ḟ = 0, we can deduce that: By designing an appropriate interference observer gain, the observation error can be made to converge exponentially. However, it is difficult to obtain the acceleration of each joint during the actual movement of the robotic arm, therefore, the following definition is given: In the formula: z is a defined auxiliary variable; p(q, q̇) is a defined nonlinear function; From equations (13) to (17), the designed interference observer is: Therefore, after adopting the disturbance observer, the composite disturbance is reduced from f to F; the dynamic equation of the robotic arm based on the disturbance observer is: 。 4. The adaptive fractional-order sliding membrane control method for a rehabilitation robot based on an interference observer according to claim 3, characterized in that, The fractional-order synovial controller and synovial convergence rate are designed as follows: Define the robotic arm trajectory tracking error as: In the formula: These are the angular displacement, angular velocity, and angular acceleration of the reference trajectory, respectively. To improve the transient performance of the sliding diaphragm control and suppress the jitter of the control system, a fractional-order sliding diaphragm control law is designed as follows: Among them, μ∈(1,2), λ∈(1,2), α = diag(α1, α2, ···,α n ) > 0, β = diag(β1, β2, ···, β n ) > 0 are all parameters to be designed; sign represents the sign function; D u- 1 e is the fractional derivative of the error e; The fractional operators are defined as follows: The dynamic equations of the robotic arm based on the interference observer established by equation (19) are as follows: Based on equations (21) to (23), we can obtain: The sliding contact rate of the control system is the exponential rate of convergence. Therefore, based on equations (24) and (25), the system control law is designed as: τ = τ eq + τ u + τ f ; Equivalent control law τ eq for: Robust control law τ u for: Disturbance suppression control law τ f for: Where v represents the item to be designed.

5. The adaptive fractional-order sliding membrane control method for a rehabilitation robot based on an interference observer according to claim 4, characterized in that, The adaptive law design for the control system is as follows: Based on equations (24) to (28), we have: Let the uncertainty disturbance Γ = -M0(q) －1 F, The estimated value is given, and the deviation between the actual value and the estimated value is defined as follows: ; To obtain the estimated uncertainty perturbation, the Lyapunov function is defined as follows: In the formula: All elements are positive values; Differentiating the Lyapunov function, we get: Based on Lyapunov's second stability theorem, design an adaptive law for the control system: , ,have: According to Lyapunov's second stability theorem, the selected Lyapunov function satisfies V ≥ 0 and V̇ ≤ 0, therefore the closed-loop control system is asymptotically stable. To reduce the jitter effect associated with the sign function, the parameter k1, representing the uncertainty limit, can be selected using the following adaptive estimate: Where η is a positive parameter; To further suppress the jitter caused by the sign function sign(s) in the sluice control law, the switching function in the control law is replaced by a smooth hyperbolic function tanh(s); In summary, the control law of the robotic arm system is: 。

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