A tracking control method for omnidirectional wheel rehabilitation robot to suppress jitter in rotation direction.

Abstract

This invention relates to the control of omnidirectional wheeled mobile robots, and more particularly to a tracking control method for an omnidirectional wheeled rehabilitation robot that suppresses jitter in the direction of rotation. It can improve system tracking accuracy, training comfort, and overall performance. The method includes: S1, establishing a grounding characteristic model based on the structural characteristics of the omnidirectional wheel, including the periodic change of the lever arm caused by the switching of contact points of the driven wheel, to obtain the robot system's dynamic equations; S2, constructing a nonlinear disturbance observer that does not require acceleration feedback; S3, employing an integral high-order sliding mode control method, decomposing the system into multiple subsystems through backstepping, and designing a tracking controller for the robot system; S4, acquiring motor state information in real time through an embedded controller, and generating control signals using the nonlinear disturbance observer and tracking controller to drive the omnidirectional wheeled rehabilitation robot to achieve trajectory tracking.

Description

Technical Field

[0001] This invention relates to the control of omnidirectional wheeled mobile robots, and more particularly to a tracking control method for an omnidirectional wheeled rehabilitation robot that suppresses jitter in the direction of motion rotation. Background Technology

[0002] In recent years, with the increasing trend of population aging and the growing demand for postoperative rehabilitation, the importance of rehabilitation robots in the field of assistive medical care has become increasingly prominent. Omnidirectional wheeled rehabilitation robots, as training devices that assist patients in achieving multi-directional movement, help users regain walking function through lower limb support and gait simulation. In this type of system, trajectory tracking accuracy is a core indicator for evaluating its performance, directly related to the safety and effectiveness of rehabilitation training.

[0003] Sliding mode control is widely used in robot motion control due to its strong robustness against disturbances and model uncertainties. However, traditional sliding mode control still has certain limitations in achieving high-precision trajectory tracking, especially the tendency to chatter, which affects system stability. Higher-order sliding mode control not only maintains the robustness of traditional methods but also effectively suppresses chatter near the sliding surface, significantly improving the smoothness and tracking accuracy of the control system.

[0004] While omnidirectional wheel mechanisms endow rehabilitation robots with omnidirectional mobility, the unique mechanical structure and the influence of human-robot interaction forces easily lead to significant jitter in the direction of rotation. This jitter intensifies with increasing applied force, severely reducing trajectory tracking accuracy and the training experience. Although numerous studies have been conducted on trajectory tracking control for omnidirectional wheel rehabilitation robots, most have not addressed the jitter issue in rotation direction through in-depth analysis and control design. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by providing a tracking control method for omnidirectional wheel rehabilitation robots that suppresses jitter in the direction of motion rotation. Starting from the grounding characteristics of the omnidirectional wheel, and combining high-order sliding mode control with nonlinear disturbance observer technology, it proposes a tracking control method aimed at suppressing jitter in the direction of motion rotation. This method aims to improve system tracking accuracy, training comfort, and overall performance, and is of great significance for the improvement of rehabilitation robot control technology.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: a tracking control method for an omnidirectional wheel rehabilitation robot to suppress jitter in the direction of motion rotation, comprising:

[0007] S1. Based on the structural characteristics of the omnidirectional wheel, a grounding characteristic model is established, including the periodic change of the lever arm caused by the switching of the contact point of the driven wheel, in order to obtain the dynamic equation of the robot system; the grounding characteristic model is used to characterize the influence of the change of the lever arm on the system dynamics during the motion process;

[0008] S2. Construct a nonlinear disturbance observer that does not require acceleration feedback; used to estimate system disturbances caused by grounding characteristics in real time, and to ensure the global uniformity and eventual boundedness of the estimation error under the condition that the rate of change of disturbance is bounded.

[0009] S3. An integral high-order sliding mode control method is adopted. The system is decomposed into multiple subsystems by backstepping. A tracking controller is designed for the robot system. The tracking controller uses the disturbance estimated by the aforementioned nonlinear disturbance observer as a feedforward compensation term to suppress the jitter in the motion rotation direction caused by the grounding characteristics and to ensure the global asymptotic stability of the closed-loop tracking system.

[0010] S4. The embedded controller collects motor status information in real time, combines it with the target trajectory command, and uses the nonlinear interference observer and tracking controller to generate control signals to drive the omnidirectional wheel rehabilitation robot to achieve trajectory tracking.

[0011] Furthermore, the establishment of the grounding characteristic model in S1 specifically includes:

[0012] S1.1 Establish the basic dynamic equations using the robot's center of gravity coordinates as state variables;

[0013] S1.2. The basic dynamic equations are converted into state-space equations with the robot's center coordinates as state variables to obtain the ideal dynamic model;

[0014] S1.3. Introduce a grounding characteristic disturbance matrix into the ideal dynamic model to construct a modified dynamic equation, i.e., a grounding characteristic model, to characterize the influence of periodic changes in the lever arm.

[0015] Furthermore, the grounding characteristic disturbance matrix is ​​a time-varying matrix whose element values ​​are related to the rotation angle of the omnidirectional wheel; the matrix is ​​used to correct the ideal generalized force mapping relationship in the ideal dynamic model to a real mapping relationship that includes the influence of periodic changes in the lever arm.

[0016] Specifically, a grounding characteristic model of the omnidirectional wheel rehabilitation robot is established.

[0017] 1. Establishment of the basic dynamic equations.

[0018] Ignoring the impact of the omnidirectional wheel's grounding characteristics, we treat the robot and its user as a single entity, and use the robot's center of gravity coordinate X... G =[x G y G θ] T As a state variable, x G y G Let θ be the coordinates of the center of gravity in the absolute coordinate system, and θ be the robot's orientation angle.

[0019] Based on Lagrange mechanics, establish the fundamental dynamic equations of the system:

[0020]

[0021] The above formula can be simplified to:

[0022] in, This is the inertia matrix of the omnidirectional wheeled rehabilitation robot (with the center of gravity as the coordinate system) during use, where M is the mass of the robot, m is the mass of the user, and r0 is the distance between the robot's center of gravity and the center. The moment of inertia of the omnidirectional wheeled rehabilitation robot about its center of gravity;

[0023] The acceleration vector of the center of gravity;

[0024] This is the lever arm matrix without considering the grounding characteristics of the omnidirectional wheel, F(t)=[f1f2f3f4] T In the diagram, f1, f2, f3, and f4 represent the driving force of each omnidirectional wheel; together they constitute a generalized force vector.

[0025] 2. Convert it into a dynamic equation with the robot's center as the state variable (i.e., an ideal dynamic model).

[0026] The center position of the omnidirectional wheel rehabilitation robot is more likely to reflect its motion characteristics than the center of gravity position. The basic dynamic equations are transformed into dynamic equations with the center as the state variable, which is the ideal dynamic model.

[0027] The relationship between the velocities at the center of gravity and the center of gravity is as follows:

[0028]

[0029] Where x(t), y(t), and θ(t) are the coordinates of the robot's center on the X-axis, Y-axis, and directional rotation angle θ, respectively. Substituting this relationship into the basic dynamic equations, we obtain the ideal dynamic model as follows:

[0030]

[0031] 3. Because the above model ignores the change in lever arm caused by the switching of contact points between the two rows of driven wheels when the omnidirectional wheel is grounded, a grounding characteristic disturbance matrix is ​​introduced.

[0032] Considering the influence of the grounding characteristics of the omnidirectional wheels, the distance from the grounding point of each omnidirectional wheel to its wheel center is expressed as δ. iThis indicates that the torque varies periodically with the wheel's rotation angle, and this periodic variation directly affects the efficiency of the driving torque. Therefore, a grounding characteristic disturbance matrix B needs to be introduced into the ideal dynamic model. δ (t) is used to correct the generalized force vector. The grounding characteristic disturbance matrix is:

[0033] Let B0(t) = B(t) + B δ (t), then

[0034] The revised dynamic equation, considering grounding characteristics, is as follows:

[0035]

[0036] Let τ = B(t)F(t), d = B δ Then the above formula can be expressed as: F(t) = F(t);

[0037]

[0038] Transforming the above equation into a state equation, let x1 = X(t), The grounding characteristic model is obtained as follows:

[0039]

[0040] Furthermore, the nonlinear disturbance observer is used to estimate system disturbances caused by grounding characteristics, and its design is as follows:

[0041]

[0042] in, Let Q(x1,x2) be the estimated disturbance of the nonlinear disturbance observer, Q(x1,x2) be the gain matrix of the nonlinear disturbance observer, z be the internal state vector of the nonlinear disturbance observer, f(x1,x2) be the nonlinear function to be designed, and f(x1,x2)=Q(x1,x2)M0x2, and τ be the control law to be designed.

[0043] Define the estimation error of the nonlinear disturbance observer:

[0044]

[0045] The nonlinear disturbance observer estimation error system is globally uniformly eventually bounded if the following conditions are met;

[0046] (1) Y is an invertible matrix, (2) Y + Y T -H≥0, matrix H is the positive definite symmetric matrix to be designed, (3) Assume that the rate of change of disturbance is bounded, satisfying t>0, The constraint, where k is a positive constant;

[0047] The Lyapunov function is designed as follows:

[0048]

[0049] Differentiating the above equation, we get:

[0050]

[0051] The above equation combines Schwarz's inequality and the given conditions. achievable σ1 is the largest eigenvalue of matrix M0;

[0052]

[0053] Where η is a constant greater than 0 and less than 1, and λ min (H) is the smallest eigenvalue of matrix H, from which we can obtain:

[0054]

[0055] This formula guarantees that the estimation error system of the nonlinear disturbance observer has global uniformity and eventual boundedness.

[0056] Furthermore, the tracking controller employs an integral-type high-order sliding mode control method, using the disturbance estimated by the nonlinear disturbance observer as a feedforward compensation term to suppress the jitter in the rotation direction caused by grounding characteristics; the design of the tracking controller includes the following steps:

[0057] Define the reference trajectory as X d Given X(t), the actual trajectory is X(t), the system's position tracking error is e1(t), and the system's velocity tracking error is e2(t), their relationship can be described as follows:

[0058]

[0059] The dynamic characteristics of the tracking errors e1(t) and e2(t) can be expressed as:

[0060]

[0061] The integral sliding surface is designed as follows:

[0062]

[0063] Where λ is a positive constant to be designed;

[0064] The first and second derivatives of the sliding surface in the above equation can be calculated as follows:

[0065]

[0066] Define s1 = S(t), The dynamic characteristics of the third-order sliding mode variable are obtained as follows:

[0067]

[0068] To ensure the asymptotic stability of the system, design the control law τ using the backstepping method, and design the following transformation:

[0069]

[0070] Where ν1, ν2, and ν3 are the transformed variables, and ρ1 and ρ2 are the virtual control laws to be designed. For a third-order strict feedback system, three steps are required to design the system using the backstepping method. The virtual control laws ρ1 and ρ2, as well as the final control law τ, will be derived step by step, as follows:

[0071] Step 1: Design the Lyapunov function as follows:

[0072]

[0073] Differentiate the above equation:

[0074]

[0075] Choose an appropriate virtual control law ρ1, as shown below:

[0076] ρ1=-ζ1ν1

[0077] Where ξ1 is the positive constant to be designed, and ρ1 is substituted into the formula. formula:

[0078]

[0079] From the above equation, if ν2=0, then And ν1 will asymptotically stabilize;

[0080] Step 2: Design the Lyapunov function as follows:

[0081]

[0082] Differentiate the above expression:

[0083]

[0084] Choose an appropriate virtual control law ρ2, as shown below:

[0085] ρ2=-ν1-ζ1s2-ζ2ν2

[0086] Where ζ2 is the positive parameter to be designed, and the formula for ρ2 is substituted into... The expression:

[0087]

[0088] From the above equation, if ν3=0, then Furthermore, ν1 and ν2 will asymptotically stabilize;

[0089] Step 3: Design the Lyapunov function as follows:

[0090]

[0091] Differentiate the above expression:

[0092]

[0093] according to The formula is as follows: ζ3 is the positive parameter to be designed, and the design control law τ is:

[0094]

[0095] To verify the stability of the closed-loop system, a Lyapunov function is designed:

[0096]

[0097] according to The formula, and the derivative of the above formula, is:

[0098]

[0099] Substituting the formula for the control law τ into the above equation, we get:

[0100]

[0101] In the formula for V(t), the Lyapunov function V(t) is positive semi-definite, and V(t) → ∞ as ||ν1||, ||ν2||, ||ν3|| → ∞, therefore V(t) is radially unbounded; In the formula, when When ν1, ν2, ν3 ≡ 0, we can obtain Then the largest invariant set is And there are no other circumstances that would cause Then set M is the unique maximal invariant set; according to the LaSalle invariant principle, the closed-loop system is globally asymptotically stable.

[0102] Furthermore, the embedded controller includes an STM32F407VET6 chip; the input interface of the STM32F407VET6 chip is connected to a motor encoder for real-time acquisition of motor speed and position information; the output interface of the STM32F407VET6 chip is connected to a motor drive module for outputting PWM control signals.

[0103] Furthermore, the embedded controller control method includes:

[0104] Receive the given target trajectory command X d (t) and

[0105] The feedback signal from the motor encoder is read, and the error between the actual trajectory and the reference trajectory is calculated.

[0106] Based on the error, combined with the disturbance feedforward compensation amount estimated by the nonlinear disturbance observer, and calculated by the integral high-order sliding mode tracking controller, the motor control quantity is generated.

[0107] The motor control signal is converted into a PWM signal, which drives the DC motor via the motor drive module, enabling the omnidirectional wheel rehabilitation robot to track the target trajectory.

[0108] Compared with the prior art, the present invention has the following advantages.

[0109] This invention establishes an omnidirectional wheel grounding characteristic model and designs a nonlinear interference observer, which can accurately estimate and compensate for periodic disturbances caused by the switching of contact points of driven wheels and human-machine interaction forces, thereby significantly suppressing the jitter phenomenon in the robot's rotation direction and improving the accuracy and stability of trajectory tracking.

[0110] This invention combines integral high-order sliding mode control with an inverse step structure to achieve robust control over complex disturbances without the need for acceleration feedback. It effectively avoids chattering issues common in traditional sliding mode control, ensuring global asymptotic stability of the closed-loop system, adapting to varying patient interaction forces, and exhibiting high reliability. Furthermore, this method actively suppresses vibrations caused by the coupling of mechanical structures and external forces at the control level, improving not only the robot's tracking performance but also significantly enhancing patient comfort and safety during training, thus contributing to improved rehabilitation outcomes. Attached Figure Description

[0111] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The scope of protection of the present invention is not limited to the following description.

[0112] Figure 1 This is a block diagram of the control system of the present invention;

[0113] Figure 2This is a model diagram of the omnidirectional wheel in this invention;

[0114] Figure 3 This is a diagram showing the change in the lever arm of the omnidirectional wheel in this invention;

[0115] Figure 4 This is a model diagram of the omnidirectional wheel rehabilitation robot in this invention;

[0116] Figure 5 This is the minimum system diagram of the STM32F407VET6 microcontroller of this invention;

[0117] Figure 6 This is a circuit diagram of the MPU9250 of the present invention;

[0118] Figure 7 This is a circuit diagram of the motor drive module of the present invention;

[0119] Figure 8 This is the overall hardware circuit diagram of the present invention. Detailed Implementation

[0120] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0121] The terminology used in the embodiments of this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of this disclosure. The singular forms “a,” “the,” and “the” as used in the embodiments of this disclosure and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0122] Depending on the context, words such as “if” or “suppose” used here can be interpreted as “when”, “in response to determination”, or “in response to detection”.

[0123] For ease of understanding, the embodiments of this disclosure will be described in detail first.

[0124] like Figure 1 As shown, a tracking control method for an omnidirectional wheel rehabilitation robot is used to suppress jitter in the direction of motion rotation.

[0125] The method specifically includes the following steps:

[0126] Step 1: Based on the structural characteristics of the omnidirectional wheel, establish a grounding characteristic model that includes the periodic change of the lever arm caused by the switching of the contact point of the driven wheel, so as to obtain the dynamic equation of the robot system; that is, the grounding characteristic model is used to characterize the influence of the change of the lever arm on the dynamics of the system during the motion.

[0127] Step 2: Construct a nonlinear disturbance observer without acceleration feedback; (used for real-time estimation of system disturbances caused by grounding characteristics, and ensuring the global consistency and eventual boundedness of the estimation error under the condition that the rate of change of disturbance is bounded;)

[0128] Step 3: Using an integral high-order sliding mode control method, the system is decomposed into multiple subsystems through backstepping. A tracking controller is designed for the robot system. The tracking controller uses the disturbance estimated by the aforementioned nonlinear disturbance observer as a feedforward compensation term to suppress the jitter in the motion rotation direction caused by the grounding characteristics and to ensure the global asymptotic stability of the closed-loop tracking system.

[0129] Step 4: The embedded controller collects motor status information in real time, combines it with the target trajectory command, and uses the nonlinear interference observer and tracking controller to generate control signals to drive the omnidirectional wheel rehabilitation robot to achieve trajectory tracking.

[0130] like Figure 2 As shown, in this embodiment, the omnidirectional wheel can be a Mecanum wheel. Because a Mecanum wheel consists of two rows of small wheels, it can move in any direction, making it suitable for lateral movement simulation in rehabilitation training. However, when grounded, the contact point between the wheel and the ground constantly switches, causing a periodic change in the lever arm length, which may lead to movement vibration. That is, the grounding characteristic of an omnidirectional wheel is that the two rows of driven wheels switch their contact points with the ground, δ... i This refers to the distance from the contact point of each omnidirectional wheel to the center of each omnidirectional wheel, such as... Figure 3 As shown, the lever arm of the wheel will vary around a constant, which can cause deviations in the tracking path. Therefore, this invention first establishes an accurate mechanical model and designs a nonlinear observer to estimate grounding interference without requiring an acceleration signal. Finally, a sliding mode algorithm and backstepping method are used to suppress jitter, ensuring tracking accuracy and stability.

[0131] One possible implementation, such as Figure 4 As shown, the omnidirectional wheeled rehabilitation robot model is illustrated, where ∑(x,O,y) is the absolute coordinate system of the system, ∑(x',O,y') is the translational coordinate system of the system, and v is the velocity of the omnidirectional wheeled rehabilitation robot. i f is the speed of the omnidirectional wheel. iThe driving force on each omnidirectional wheel is given by: G = robot's center of gravity during operation, C = robot's center, r0 = distance between robot's center of gravity and center, α = angle between x' axis and v direction, β = angle between x' axis and r0 direction, and L = distance from robot's center of gravity to each omnidirectional wheel. i θ is the distance from the center of gravity to the center of gravity for each omnidirectional wheel. i φ is the angle between the x' axis and the positions of each omnidirectional wheel. i x' axis and l i The included angle.

[0132] According to such Figure 3 The omnidirectional wheel rehabilitation robot model shown is combined with the Lagrange dynamics equation (1) to derive the dynamic equation (7) of the robot with the robot's center of gravity coordinates as its state when in use, and the dynamic equation (10) of the robot with the robot's center coordinates as its state.

[0133] The Lagrange dynamics equations are described as follows:

[0134]

[0135] Where L = QP, Q is the total kinetic energy of the system, P is the total potential energy of the system, and τ is the driving torque of the system;

[0136] Therefore, the total kinetic energy of the omnidirectional wheel rehabilitation robot can be expressed as:

[0137]

[0138] Here, the robot's center of gravity, under the influence of the human, is located at position X. G =[x G y G θ] T M is the mass of the robot, and m is the mass of the user;

[0139] Since the omnidirectional wheel rehabilitation robot operates on a flat surface, its potential energy P = 0, therefore:

[0140]

[0141] besides:

[0142]

[0143] Substituting formula (4) into formula (1) yields:

[0144]

[0145] Here, Given the rotational inertia of the omnidirectional wheel rehabilitation robot, analyzing its coordinate system yields the driving torque expressed as:

[0146]

[0147] Therefore, considering the influence of the omnidirectional wheel's grounding characteristics, the dynamic equation of the omnidirectional wheel rehabilitation robot during use, with the robot's center of gravity coordinates as the state variable, can be expressed as:

[0148]

[0149] The above dynamic equations can be simplified as follows:

[0150]

[0151] in, This is the inertia matrix of the omnidirectional wheeled rehabilitation robot during use. This is the lever arm matrix considering the ground contact characteristics of the omnidirectional wheel, F(t)=[f1f2f3f4] T Where f1, f2, f3, and f4 represent the driving force of each omnidirectional wheel.

[0152] During trajectory tracking, the omnidirectional wheel rehabilitation robot is considered as a particle, and the robot's center position is considered the system state. Because the omnidirectional wheel rehabilitation robot is symmetrical in shape, the center position more accurately reflects its motion characteristics than the center of gravity position. Therefore, the system state of the omnidirectional wheel rehabilitation robot is converted from the center of gravity position during use to the center position. Under human intervention, the velocity relationship between the omnidirectional wheel rehabilitation robot at the center of gravity and the center position is expressed as:

[0153]

[0154] Where x(t), y(t), and θ(t) are the coordinates of the robot center on the X-axis, Y-axis, and directional rotation angle θ, respectively. Substituting equation (9) into equation (8) yields the dynamic equation with the robot center coordinates as the state:

[0155]

[0156] Let τ = B(t)F(t), d = B δ (t)F(t);

[0157] Where B0(t)=B(t)+B δ (t), It is the grounding characteristic disturbance matrix.

[0158] The omnidirectional wheeled rehabilitation robot, with its central coordinates as its state, can be represented by the following dynamic equation considering grounding characteristics:

[0159]

[0160] Transform formula (11) into a state-space equation, and let x1 = X(t). have to:

[0161]

[0162] Specifically, step 1 is used to establish an accurate dynamic model. First, a robot dynamic model is established, and models are built with the center of gravity and center as state variables respectively. Then, a grounding characteristic matrix is ​​introduced to describe the impact of lever arm changes, finally obtaining the state equation, which facilitates controller design. That is, this step incorporates the periodic changes in lever arm caused by the switching of contact points of the driven wheels in the actual system into the model by introducing a grounding characteristic disturbance matrix, thereby more realistically reflecting the dynamic characteristics of the system. This model not only lays the foundation for the subsequent design of disturbance observers and controllers, but also provides a theoretical basis for suppressing rotational jitter.

[0163] In step 2, to address the issue of motion rotation direction jitter in the omnidirectional wheel rehabilitation robot during human-computer interaction, a nonlinear disturbance observer that does not require real-time acceleration information feedback is designed based on the omnidirectional wheel grounding characteristic model. This observer ensures that the estimation error has global uniformity and eventual boundedness under the condition that the disturbance change rate norm is bounded.

[0164] In other words, based on the grounding characteristic model established in step 1, this step designs a nonlinear disturbance observer that does not require acceleration feedback, used to estimate system disturbances caused by grounding characteristics in real time. Since acceleration signals are difficult to measure directly and easily introduce noise, this observer estimates disturbances indirectly through system state and input information, avoiding the shortcomings of acceleration feedback. This observer is closely integrated with the model in step 1, utilizing model information to improve estimation accuracy and providing accurate feedforward compensation signals for the subsequent controller, thereby effectively suppressing periodic disturbances caused by grounding characteristics.

[0165] Another possible implementation: When a patient actually uses the omnidirectional wheel rehabilitation robot, the grounding characteristics of the omnidirectional wheel can reduce the system's control accuracy and increase system chattering, leading to deviations in trajectory tracking. Considering that acceleration information is difficult to measure directly from an accelerometer, and that the derivative of acceleration and velocity information can easily introduce high-frequency noise, even causing system instability, a nonlinear interference observer is designed to estimate the grounding characteristics of the omnidirectional wheel as interference.

[0166]

[0167] in, Let Q(x1,x2) be the gain matrix of the nonlinear disturbance observer, z be the internal state vector of the nonlinear disturbance observer, and f(x1,x2) be the nonlinear function to be designed. The specific design steps of the nonlinear disturbance observer are as follows:

[0168] ① Construct the auxiliary function as follows:

[0169]

[0170] To avoid introducing acceleration information, the following function is designed:

[0171] f(x1,x2)=Q(x1,x2)M0x2 (15)

[0172] ② Design the nonlinear disturbance observer structure as follows:

[0173]

[0174] The structure of the nonlinear disturbance observer can be obtained as follows:

[0175]

[0176] ③ Define the estimation error of the nonlinear disturbance observer:

[0177]

[0178] Assuming the rate of change of the disturbance is bounded, satisfying t > 0, The constraint, where k is a positive constant;

[0179]

[0180] The following theorem states that a nonlinear disturbance observer estimation error system is globally uniformly eventually bounded if the following conditions are met.

[0181] (1) Y is an invertible matrix, (2) Y + Y T -H≥0, matrix H is the positive definite symmetric matrix to be designed, (3) the rate of change of disturbance satisfies the assumption;

[0182] The Lyapunov function is designed as follows:

[0183]

[0184] Since the inertia matrix M0 is a positive definite matrix and Y is an invertible matrix, then Y T M0Y is also a positive definite matrix, and V(t) is also a positive definite function. Taking the derivative of formula (20) gives:

[0185]

[0186] Formula (21) combines the Schwarz inequality and the given conditions We can obtain,

[0187] σ1 is the largest eigenvalue of matrix M0;

[0188]

[0189] Where η is a constant that is greater than 0 and less than 1, λ min (H) is the smallest eigenvalue of matrix H, from which we can obtain:

[0190]

[0191] Therefore, equation (23) proves that the nonlinear disturbance observer estimation error system is globally uniformly bounded and converges to a radius of 2kσ1||Y|| 2 / ηλ min (Q) within the sphere.

[0192] Step 3: Adopting the integral-type high-order sliding mode control theory, for the dynamic system of trajectory tracking error, the complex system is decomposed into multiple independent subsystems using the backstepping method. A motion rotation direction jitter suppression controller with global asymptotic stability is designed using Lyapunov theory. Based on the disturbance estimation information provided in Step 2, this step further designs an integral-type high-order sliding mode tracking controller, decomposing the system into multiple subsystems and designing the control law step by step using the backstepping method. This controller fully utilizes the disturbance feedforward compensation provided by the nonlinear disturbance observer, combined with the strong robustness of the integral sliding surface and the stability guarantee of the backstepping method, effectively suppressing rotation direction jitter and improving trajectory tracking accuracy. This step is closely integrated with Step 2, forming an integrated framework of observation-compensation-control, jointly improving the control performance and stability of the system.

[0193] The reference trajectory is defined as X d The tracking errors e1(t) and e2(t) of the system are expressed as:

[0194]

[0195] The dynamic characteristics of the tracking errors e1(t) and e2(t) can be expressed as:

[0196]

[0197] The integral sliding surface is designed as follows:

[0198]

[0199] Where λ is a positive constant to be designed;

[0200] Then the first and second derivatives of the sliding surface in formula (26) can be calculated as follows:

[0201]

[0202] Define s1 = S(t), The dynamic characteristics of the third-order sliding mode variable can be obtained as follows:

[0203]

[0204] To ensure the asymptotic stability of the system, the control law τ can be designed using the backstepping method, and the following transformation can be designed:

[0205]

[0206] Where ν1, ν2, and ν3 are the transformed variables, and ρ1 and ρ2 are the virtual control laws to be designed. Based on formulas (27) and (28), for the third-order strict feedback system formula (28), three steps need to be designed according to the backstepping method. The virtual control laws ρ1 and ρ2, as well as the final control law τ, will be derived step by step. The steps are as follows:

[0207] Step 1: Design the Lyapunov function as follows:

[0208]

[0209] Differentiate equation (30):

[0210]

[0211] Choose an appropriate virtual control law ρ1, as shown below:

[0212] ρ1=-ζ1ν1 (32)

[0213] Where ζ1 is the positive constant to be designed, substituting formula (32) into formula (31):

[0214]

[0215] From formula (33), if ν2=0, then And ν1 will asymptotically stabilize;

[0216] Step 2: Design the Lyapunov function as follows:

[0217]

[0218] Differentiate formula (34):

[0219]

[0220] Choose an appropriate virtual control law ρ2, as shown below:

[0221] ρ2=-ν1-ζ1s2-ζ2ν2 (36)

[0222] Where ζ2 is the positive parameter to be designed, substituting formula (36) into formula (35):

[0223]

[0224] From formula (37), if ν3=0, then Furthermore, ν1 and ν2 will asymptotically stabilize;

[0225] Step 3: Design the Lyapunov function as follows:

[0226]

[0227] Differentiate formula (38):

[0228]

[0229] According to formula (39), the control law τ can be designed:

[0230] τ=τ0+τ1+τ2 (40)

[0231] Where τ0 deals with the known part, τ1 is the term that stabilizes the entire system, and τ2 is the term that compensates for unknown uncertainties. Therefore, the corresponding equations for τ0 and τ1 are as follows:

[0232]

[0233] Where ζ3 is the positive parameter to be designed. Therefore, the designed control law τ is:

[0234]

[0235] To verify the stability of the closed-loop system, a Lyapunov function is designed:

[0236]

[0237] According to formula (39), the derivative of formula (43) is:

[0238]

[0239] Substitute formula (42) into formula (44):

[0240]

[0241] In formula (43), the Lyapunov function V(t) is positive semi-definite. When ||ν1||, ||ν2||, ||ν3|| → ∞, V(t) → ∞, so V(t) is radially unbounded. In formula (45), when When ν1, ν2, ν3 ≡ 0, we can obtain Then the largest invariant set is And there are no other circumstances that would cause Then set M is the unique maximal invariant set; according to the LaSalle invariant principle, the closed-loop system is globally asymptotically stable.

[0242] As another possible embodiment, such as Figure 5-8 As shown, the STM32F407VET6 chip outputs a PWM signal to the motor drive module, enabling the omnidirectional wheeled rehabilitation robot to help random trainees track training trajectories specified by doctors. The STM32F407VET6 chip is the main controller, with its input connected to the motor speed measurement module and its output connected to the motor drive module. The motor drive module is connected to the DC motor, and the power supply system provides power to all electrical devices. The main controller's control method involves reading the feedback signal from the motor encoder and the control command signal X given by the main controller. d (t) and The error signal is calculated. Based on the error signal, the main controller calculates the control quantity of the motor according to the predetermined control algorithm and sends it to the motor drive module. The motor rotates to drive the wheels to maintain their own balance and move in a specified manner.

[0243] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "illustrative embodiment," "preferred embodiment," "detailed description," or "preferred embodiment," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0244] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Therefore, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A tracking control method for an omnidirectional wheel rehabilitation robot to suppress jitter in the direction of motion rotation, characterized by: include: S1. Based on the structural characteristics of the omnidirectional wheel, a grounding characteristic model is established, including the periodic change of the lever arm caused by the switching of the contact point of the driven wheel, in order to obtain the dynamic equation of the robot system. S2. Construct a nonlinear disturbance observer that does not require acceleration feedback; S3. An integral high-order sliding mode control method is adopted. The system is decomposed into multiple subsystems by backstepping. A tracking controller is designed for the robot system. The tracking controller uses the disturbance estimated by the aforementioned nonlinear disturbance observer as a feedforward compensation term to suppress the jitter in the motion rotation direction caused by the grounding characteristics and to ensure the global asymptotic stability of the tracking controller. S4. Real-time acquisition of motor status information through embedded controller, combined with target trajectory instructions, and control signal generated by the nonlinear interference observer and tracking controller to drive the omnidirectional wheel rehabilitation robot to achieve trajectory tracking. The nonlinear disturbance observer is used to estimate system disturbances caused by grounding characteristics, and its design is as follows: in, For the estimation of disturbance by the nonlinear disturbance observer, Here is the gain matrix of the nonlinear disturbance observer. Let be the internal state vector of the nonlinear disturbance observer. Let be the nonlinear function to be designed, and , The control law to be designed; where, , , , , , The Robot Center is located in axis, Axis, direction angle The coordinates on; where, It is the inertia matrix of the omnidirectional wheeled rehabilitation robot during use, and among them, It's about the quality of the robot. It is the quality of the user. The distance between the robot's center of gravity and the center. The moment of inertia of the omnidirectional wheeled rehabilitation robot about its center of gravity; Define the estimation error of the nonlinear disturbance observer: Among them, nonlinear interference ;in And among them (t), (t), (t), (t) represents the distance from the contact point of each of the four omnidirectional wheels to the center of the wheel, where t is a time variable; middle, , , , This indicates the driving force of each omnidirectional wheel; The nonlinear disturbance observer estimation error system is globally uniformly eventually bounded if the following conditions are met; (1) It is an invertible matrix, (2) ,matrix It is the positive definite symmetric matrix to be designed. (3) Assume that the rate of change of the disturbance is bounded and satisfies hour, The constraints, among which It is a positive number; The Lyapunov function is designed as follows: Differentiating the above equation, we get: The above equation combines Schwarz's inequality and the given conditions. achievable , It is a matrix The largest eigenvalue; in, It is a constant greater than 0 and less than 1. For matrix The smallest eigenvalue can be obtained as follows: This formula guarantees that the estimation error system of the nonlinear disturbance observer has global uniformity and eventual boundedness.

2. The tracking control method for an omnidirectional wheel rehabilitation robot with motion rotation direction jitter suppression according to claim 1, characterized in that: The specific steps involved in establishing the grounding characteristic model in S1 are: S1.1 Establish the basic dynamic equations using the robot's center of gravity coordinates as state variables; S1.

2. The basic dynamic equations are converted into dynamic equations with the robot's center coordinates as variables to obtain an ideal dynamic model; S1.

3. Introduce a grounding characteristic disturbance matrix into the ideal dynamic model to construct a modified dynamic equation, i.e., a grounding characteristic model, to characterize the influence of periodic changes in the lever arm.

3. The tracking control method for an omnidirectional wheel rehabilitation robot with motion rotation direction jitter suppression according to claim 2, characterized in that: The grounding characteristic disturbance matrix is ​​a time-varying matrix whose element values ​​are related to the rotation angle of the omnidirectional wheel; the matrix is ​​used to correct the ideal generalized force mapping relationship in the ideal dynamic model to a real mapping relationship that includes the influence of periodic changes in the lever arm.

4. The tracking control method for an omnidirectional wheel rehabilitation robot with motion rotation direction jitter suppression according to claim 1, characterized in that: The embedded controller includes an STM32F407VET6 chip; the input interface of the STM32F407VET6 chip is connected to a motor encoder for real-time acquisition of motor speed and position information; the output interface of the STM32F407VET6 chip is connected to a motor drive module for outputting PWM control signals.

5. The tracking control method for an omnidirectional wheel rehabilitation robot with motion rotation direction jitter suppression according to claim 4, characterized in that: The embedded controller control method includes: Receive the given target trajectory instruction; The feedback signal from the motor encoder is read, and the error between the actual trajectory and the reference trajectory is calculated. Based on the error, combined with the disturbance feedforward compensation amount estimated by the nonlinear disturbance observer, and calculated by the integral high-order sliding mode tracking controller, the motor control quantity is generated. The motor control signal is converted into a PWM signal, which drives the DC motor via the motor drive module, enabling the omnidirectional wheel rehabilitation robot to track the target trajectory.

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