An unknown nonlinear dynamic approximation method for lower extremity exoskeleton robot

Abstract

This invention discloses a method for approximating unknown nonlinear dynamics in a lower limb exoskeleton robot, comprising: designing an estimation law for the approximation error term of the unknown nonlinear dynamics; estimating the ideal weights of the neural network; and estimating the error term based on the designed estimation law for the approximation error of the unknown nonlinear dynamics, thereby obtaining a new neural network approximator to approximate the unknown nonlinear dynamics. This invention employs the gradient descent method to estimate the ideal weights of the neural network and estimates the error term based on the designed estimation law for the approximation error of the unknown nonlinear dynamics, thus obtaining a new neural network approximator, which is used to approximate the unknown nonlinear dynamics. It also proposes that when the adaptive parameter approaches positive infinity, the error exponent converges to zero. Based on the unknown nonlinear dynamics approximated by the new neural network approximator, a more accurate model of the lower limb exoskeleton robot system is established. The control scheme designed based on this model can achieve real-time control of the system, thereby improving the system's stability, safety, and the comfort of human-computer interaction, and ultimately increasing user compliance and participation.

Description

Technical Field

[0001] This invention relates to an unknown nonlinear dynamic approximation method for lower limb exoskeleton robots, belonging to the field of lower limb exoskeleton robot control technology. Background Technology

[0002] Exoskeletons are wearable robots with significant advantages such as wear resistance, intelligence, ease of operation, and high rigidity. They can be divided into upper limb and lower limb exoskeletons and represent a high-end technology in the mechanical field, with wide applications in military, medical, and rescue sectors. For example, in the military, exoskeletons allow soldiers to carry more combat supplies with less physical exertion, while also improving battlefield mobility, which is crucial for individual soldier combat. In the medical field, lower limb exoskeletons are mainly used for rehabilitation training, eliminating the reliance on and limitations of traditional rehabilitation methods such as physician-level expertise. However, the safety, comfort, and efficiency of lower limb exoskeletons are directly affected by their control strategies. Undesirable interaction loads caused by human-machine incompatibility can lead to negative training effects and even limb injuries. The accuracy of the established lower limb exoskeleton system model indirectly plays a decisive role in the design of the control scheme, the safety of the lower limb exoskeleton system, and user compliance and participation.

[0003] For lower limb exoskeletons in the medical field, the existence of unknown nonlinear dynamics, along with factors such as peculiar user gait and varying limb swing amplitudes among different users, often leads to discrepancies between the established lower limb exoskeleton system model and the real system. This discrepancy is undoubtedly something that controller design must strive to avoid. From the perspective of ensuring that exoskeleton movement does not cause harm to the user, the control scheme must guarantee that the exoskeleton movement conforms to human movement mechanisms. Therefore, how to handle the unknown nonlinear dynamics in the system and avoid these uncertainties, as well as the user's recoil and unexpected limb torque that could cause injury, becomes particularly important.

[0004] In existing lower limb exoskeleton systems, to maintain good dynamic performance, control laws need to be designed based on the dynamic characteristic model of the lower limb exoskeleton. However, the dynamic characteristic model of the lower limb exoskeleton is a complex nonlinear system with multiple inputs and outputs and unknown nonlinear dynamics. To approximate the dynamic model of the lower limb exoskeleton robot system, methods such as least squares and fuzzy logic systems are currently mainly used to handle the unknown dynamics in the nonlinear system. However, the least squares method will experience data saturation, at which point a forgetting factor must be added. When the forgetting factor is larger, the parameter identification results are more stable, but the response speed is slower, the real-time performance is poor, and the model accuracy is not optimal. When the forgetting factor is smaller, the parameter identification results fluctuate greatly, but the response speed is fast and the model accuracy is high. The fuzzy approximation method mainly handles the unknown dynamics by accurately approximating the fuzzy ideal weights and adjusting the controller parameters. Although it can ultimately achieve a relatively ideal control effect, it is difficult to approximate the unknown dynamics with high precision. This is not conducive to designing control schemes and realizing real-time control of the body. At the same time, the uncertainty of dynamically changing parameters such as inertia matrix and rotation matrix, as well as other unknown nonlinear dynamics that we have not yet discovered, all contribute to the inaccuracy of the constructed model. Therefore, for unknown nonlinear dynamics, this invention proposes a solution that can approximate them with high accuracy and whose approximation error converges to zero exponentially. This is of great significance for improving the comfort of human-computer interaction and the stability of the system. Summary of the Invention

[0005] To address the unknown nonlinear dynamics present in current models of lower limb exoskeleton robots, and to improve the accuracy of these models, this invention provides a method for approximating unknown nonlinear dynamics in lower limb exoskeleton robots. The aim is to design an unknown nonlinear dynamics approximator to approximate the unknown nonlinear dynamics in the lower limb exoskeleton robot system with high accuracy.

[0006] The technical solution of this invention is:

[0007] According to a first aspect of the present invention, an unknown nonlinear dynamic approximation method for a lower limb exoskeleton robot is provided, comprising: designing an estimation law for the unknown nonlinear dynamic approximation error term; estimating the ideal weights of the neural network; and estimating the error term based on the designed unknown nonlinear dynamic approximation error estimation law to obtain a new neural network approximator to approximate the unknown nonlinear dynamic.

[0008] The estimation law for the unknown nonlinear dynamic approximation error term is described. Specifically:

[0009]

[0010] Wherein, the adaptive parameter K > 0; It is an estimate of the unknown ideal weight vector; Let S(x) be an auxiliary variable representing S(x), where S(x) is a basis vector. and These are auxiliary variables x and u, respectively, where x is the system output and u is the input.

[0011] The estimation of the ideal weights of the neural network specifically involves using the gradient descent algorithm to estimate the ideal weights of the neural network.

[0012] The gradient descent algorithm is used to estimate the ideal weights of the neural network, and the expression is as follows:

[0013]

[0014] Where γ represents the neural network weight estimation parameters; x is the system output; β represents the gradient descent parameters; and S(x) is a basis vector. An estimate of the unknown ideal weight vector; for First derivative.

[0015] The new neural network approximator The expression is:

[0016]

[0017] in, Adaptive parameter K > 0; Let S(x) be an auxiliary variable representing S(x), where S(x) is a basis vector. and These are auxiliary variables x and u, respectively, where x is the system output and u is the input; It is an estimate of the unknown ideal weight vector.

[0018] According to a second aspect of the invention, a processor is provided for running a program, wherein the program, when running, executes the unknown nonlinear dynamic approximation method for a lower limb exoskeleton robot as described in any one of the preceding claims.

[0019] The beneficial effects of this invention are:

[0020] This invention employs gradient descent to estimate the ideal weights of a neural network and estimates the error term based on a designed unknown nonlinear dynamic approximation error estimation law, thereby obtaining a new neural network approximator. This new approximator is used to approximate the unknown nonlinear dynamics. It also proposes that the error exponent converges to zero when the adaptive parameter approaches positive infinity. Based on the unknown nonlinear dynamics approximated by the new neural network approximator, a more accurate model of a lower limb exoskeleton robot system is established. The control scheme designed based on this model enables real-time control of the system, thereby improving system stability, safety, and human-machine interaction comfort, ultimately increasing user compliance and engagement. Attached Figure Description

[0021] Figure 1 This is a flowchart of the present invention;

[0022] Figure 2 It is a comparison of the approximation trajectories of traditional neural networks and new neural network approximators for unknown dynamics;

[0023] Figure 3 It is a comparison of the approximation errors of traditional neural networks and new neural network approximators for unknown nonlinear dynamics. Detailed Implementation

[0024] The invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited to the description.

[0025] Example 1: As Figure 1-3 As shown, according to a first aspect of the present invention, an unknown nonlinear dynamic approximation method for a lower limb exoskeleton robot is provided, comprising: designing an estimation law for the unknown nonlinear dynamic approximation error term; estimating the ideal weights of the neural network; and estimating the error term based on the designed unknown nonlinear dynamic approximation error estimation law to obtain a new neural network approximator to approximate the unknown nonlinear dynamic.

[0026] Furthermore, the estimation law for the unknown nonlinear dynamic approximation error term is designed... Specifically:

[0027]

[0028] Wherein, the adaptive parameter K > 0; It is an estimate of the unknown ideal weight vector; Let S(x) be an auxiliary variable representing S(x), where S(x) is a basis vector. and These are auxiliary variables x and u, respectively, where x is the system output and u is the input.

[0029] Furthermore, the estimation of the ideal weights of the neural network specifically involves using a gradient descent algorithm to estimate the ideal weights of the neural network.

[0030] Furthermore, the gradient descent algorithm is used to estimate the ideal weights of the neural network, and the expression is:

[0031]

[0032] Where γ represents the neural network weight estimation parameters; x is the system output; β represents the gradient descent parameters; and S(x) is a basis vector. An estimate of the unknown ideal weight vector; for First derivative.

[0033] Furthermore, the new neural network approximator is expressed as:

[0034]

[0035] in, Adaptive parameter K > 0; Let S(x) be an auxiliary variable representing S(x), where S(x) is a basis vector. and These are auxiliary variables x and u, respectively, where x is the system output and u is the input; It is an estimate of the unknown ideal weight vector.

[0036] According to a second aspect of the present invention, a processor is provided for running a program, wherein the program executes the unknown nonlinear dynamic approximation method for a lower limb exoskeleton robot as described in any of the preceding embodiments.

[0037] The principle behind this invention is described as follows:

[0038] 1. Establish the model and describe the problem.

[0039] In this invention, a lower limb exoskeleton system with 2 degrees of freedom is considered, and its dynamic model is established based on the Euler-Lagrange equations as follows:

[0040]

[0041] Where θ = [θ1, θ2] T It is a joint angle vector, with the hip joint angle being θ1 and the knee joint angle being θ2; These are the joint angular velocity and angular acceleration vectors, respectively; τ = [τ1, τ2] T These are the input torques of the exoskeleton system; the hip joint input torque is τ1, and the knee joint input torque is τ2. h =[τh1 ,τ h2 ] T It is the torque vector of the human body, and the torque vector of the hip joint is τ. h1 The knee joint torque vector is τ h2 ; It is a generalized inertia matrix with a dimension of 2×2; It is a centripetal matrix; This represents the gravity vector. To avoid using acceleration signals, an intermediate variable is defined:

[0042]

[0043] Based on the intermediate variables, the dynamic model based on the Euler-Lagrange equations (i.e., equation (1)) can be reconstructed as follows:

[0044]

[0045] Note derivative It includes joint angle acceleration signals. Subsequent updates are performed using an adaptive law to avoid computation.

[0046] The standard neural network expression is as follows:

[0047]

[0048] in, This represents an estimate of the unknown nonlinear dynamic f(x); x = [x1, x2, ..., x...]. n ] T Let S(x) be the state vector of the system; S(x) = [s1(x),...,s...]. i (x),...,s L (x)] T (1≤i≤L) is a basis vector and and σ x >0 represents s i The center and width of (x), s i (x) is the i-th element in S(x), ||s i (x)‖≤1. In compact set The expression for approximating unknown nonlinear dynamics using a traditional neural network is as follows:

[0049] f(x) = W *T S(x)+ε (5)

[0050] in, Represents an m-dimensional real space; the unknown nonlinear dynamic approximation error ε of the system satisfies |ε|≤ε * ;ε* >0 is the upper bound of the unknown nonlinear dynamic approximation error of the system; It is an unknown ideal weight vector The estimated value, where L is the number of neural nodes; and

[0051]

[0052] The objective of this invention is to design a neural network approximator for an unknown nonlinear dynamic f(x) in a lower limb exoskeleton system. This ensures that when the adaptive parameter K approaches positive infinity, the unknown nonlinear dynamic approximation error... The exponent converges to zero.

[0053] 2. Estimation of unknown nonlinear dynamic approximation error and design of a novel neural network approximator

[0054] For the dynamic equation: (where x is the system state vector, x is the system output, f(x) is the unknown nonlinear dynamics in the system, and u is the input), first define x, s i The adaptive laws for the auxiliary variables (x) and u are as follows:

[0055]

[0056]

[0057]

[0058] Where the adaptive parameter K > 0, and They are x and s respectively i Auxiliary variables of (x) and u, These are auxiliary variables and The adaptive law, Let each of these represent the initial value of the adaptive law for each auxiliary variable. Assume the desired trajectory y... d It is n-th order differentiable and smooth and bounded. The unknown nonlinear dynamic approximation error and its derivative are both bounded. Then, the estimation law for the unknown nonlinear dynamic approximation error term is... It can be designed as:

[0059]

[0060] in, It is an unknown ideal weight vector The estimated value;

[0061]

[0062] Substituting (10) as an estimate of the unknown nonlinear dynamic approximation error ε into (5), we can obtain the new neural network approximator as follows:

[0063]

[0064] in,

[0065] The estimation law for the unknown nonlinear dynamic approximation error term and the design process of the new neural network approximator are given below:

[0066] First, the estimation law for the unknown nonlinear dynamic approximation error is designed: From equation (5) and the dynamic equation, we can obtain:

[0067]

[0068] The auxiliary function is defined as follows:

[0069]

[0070] Substituting the adaptive laws in (7)-(9) into (13) and taking the first derivative of (13) yields:

[0071]

[0072] Where K>0 is the adaptive parameter, Consider the following Lyapunov function:

[0073]

[0074] Taking its first derivative, we get:

[0075]

[0076] According to Young's inequality, equation (16) can be written as:

[0077]

[0078] Solving equation (17) yields: This means V Z Both Z and Z are bounded, and Z converges the exponent to a value that is given by the expression Z. The defined residual set, and also proves that lim K→∞ Z = 0; V Z (0) represents the constant term in the solution of a differential equation with constant coefficients; e represents the natural constant;

[0079] According to formula (13), from Z = 0, we can obtain:

[0080]

[0081] in, Let ω represent the error term of Z. Let Then (18) can be written as:

[0082]

[0083] As K approaches positive infinity, ω approaches zero. Analysis and Convergence. For Prove that any element s i The convergence of (x) can then be used to obtain the entire The convergence of . Let Consider the following Lyapunov function:

[0084]

[0085] in, s i (x) and Error term; s i Auxiliary variable of (x).

[0086] Taking the first derivative of equation (20) yields:

[0087]

[0088] in, Solving equation (21) yields This means V s It is bounded, and The exponent converges to the point where... The defined residual set, in addition, can also be proven. That is, any element It is bounded, therefore It is bounded. Using the same proof method, it can be proven that... and It is bounded; V s (0) represents the constant term in the solution of a differential equation with constant coefficients.

[0089] Next, consider the following Lyapunov function:

[0090]

[0091] Where x is the system output, Combining the aforementioned dynamic equation Define y d Let the desired trajectory be denoted as follows. Then the first derivative of equation (22) can be obtained as follows:

[0092]

[0093] Where γ represents the neural network weight estimation parameter and is >0;

[0094] The control law for input u is:

[0095]

[0096] Where k>0 are controller parameters. Substituting (24) into (23), we get:

[0097]

[0098] Depend on choose The estimation law is:

[0099]

[0100] Where β represents the gradient descent parameter and is >0;

[0101] Substituting (26) into (25), we get:

[0102]

[0103] According to Young's inequality, equation (27) can be written as:

[0104]

[0105] in, Due to W * It is bounded, therefore we can conclude that... It is bounded, that is Based on the above analysis, we can conclude that Given the bounded conclusion, substituting equation (10) into equation (5), we obtain:

[0106]

[0107] in, Thus, based on the above analysis, it can be seen that equations (10) and (11) are proven to be valid.

[0108] Considering the real-time control and stability of lower limb exoskeleton robot systems, properly handling the unknown nonlinear dynamics within the system is crucial. Currently, traditional methods primarily employ least squares and gradient descent to identify unknown parameters, then use the estimation results to compensate for the unknown nonlinear dynamics of the lower limb exoskeleton robot. This can establish a relatively accurate dynamic model, but suffers from slow response speeds and difficulty in accurately approximating the unknown dynamics. This invention differs from traditional approximation methods, effectively addressing the aforementioned problems without relying on additional observers. Furthermore, the neural network weights are directly estimated using the gradient descent algorithm, which reduces the accuracy requirements of the neural network weights and thus minimizes the impact on the approximation effect of the unknown nonlinear dynamics. When the adaptive parameter K approaches positive infinity, the approximation error of the unknown nonlinear dynamics converges exponentially to zero, indicating a fast response speed.

[0109] To approximate the real system with high accuracy, this invention designs an estimation law for the unknown nonlinear dynamic approximation error. Combined with gradient descent to estimate the neural network weights, a new neural network approximator is constructed to approximate the unknown nonlinear dynamic. As the adaptive parameter K approaches positive infinity, the approximation error of the unknown nonlinear dynamic converges exponentially to zero.

[0110] Figure 1 This patent demonstrates the method and process of approximating unknown nonlinear dynamics using a novel neural network approximator.

[0111] The effectiveness of this method is verified by the following simulation experiment based on the design of a second-order system.

[0112]

[0113] Where x1 and x2 are the system states, and f(x1, x2) is the unknown nonlinear dynamic in this system. In the simulation experiment, the unknown nonlinear dynamic is set as follows: y and u are the output and input of the system, respectively. In this example, to approximate the unknown nonlinear dynamics, 5 neural nodes are chosen, and the reference signal y is used. d =sin(t). And the control law for the input u is designed as follows:

[0114]

[0115] in, It is a virtual control law The first derivative of . e1 = yy d e2 = x2 - α are two error terms, and k > 0 are controller parameters. This is based on the newly designed neural network approximator (11) for estimating unknown nonlinear dynamics. The estimation law for the neural network weights is designed as follows:

[0116]

[0117] in, Here, S(x1,x2) represents the estimated weight vector of the neural network, S(x1,x2) is the basis function, and γ and β are the neural network weight estimation parameters and gradient descent parameters, respectively. The relevant parameters in the simulation experiment are set as follows: k = 50, K = 100, β = 1, γ = 0.01, x1(0) = 1, x2(0) = 0. Since the number of neural nodes is 5, the initial values ​​of the 5 neural network weight vector estimation laws are set to 130, 60, 20, 0, and 0, respectively. All other parameters and initial values ​​are set to 0.

[0118] Figure 2 Demonstrates the use of traditional neural networks respectively and new neural network approximators Approximating the trajectory of unknown nonlinear dynamics. It should be noted that in the process of program design, traditional neural network approximation methods only update the weights by designing a weight update law, while the new neural network approximator proposed in this invention not only has a weight update law, but also an estimation law for the approximation error of unknown nonlinear dynamics. Figure 3 This shows the approximation errors of two methods when approximating unknown nonlinear dynamics. and These are the dynamic approximation error curves of the new neural network approximator and the traditional neural network with unknown nonlinearities, respectively. Figure 2 It can be seen that the new neural network approximator has better approximation performance, and it can approximate unknown nonlinear dynamics with higher accuracy. Figure 3 The results presented further confirm this viewpoint. Furthermore, Figure 3 It also shows that the new neural network approximator has an approximation error curve that is closer to zero and has a smaller amplitude and is flatter when approximating unknown nonlinear dynamics compared to traditional neural networks, which indicates that the approximation effect is more stable.

[0119] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. An unknown nonlinear dynamic approximation method for a lower extremity exoskeleton robot, characterized by, include: Design an estimation law for the unknown nonlinear dynamic approximation error term; The ideal weights of the neural network are estimated, and the error term is estimated based on the designed unknown nonlinear dynamic approximation error estimation law. A new neural network approximator is obtained to approximate the unknown nonlinear dynamics, thereby realizing the approximation of the unknown nonlinear dynamics of the lower limb exoskeleton robot system. The estimation law for the unknown nonlinear dynamic approximation error term is described. Specifically: ； Among them, adaptive parameters ; It is an estimate of the unknown ideal weight vector; express Auxiliary variables, It is a basis vector; and They are and Auxiliary variables, This is the system output, and u is the input. The estimation of the ideal weights of the neural network specifically involves using a gradient descent algorithm to estimate the ideal weights of the neural network. The gradient descent algorithm is used to estimate the ideal weights of the neural network, and the expression is as follows: ； in, The parameters represent the weight estimation parameters of the neural network; x is the system output. Indicates the gradient descent parameters; It is a basis vector; An estimate of the unknown ideal weight vector; for First derivative; The new neural network approximator The expression is: ； in, Adaptive parameters ; express Auxiliary variables, It is a basis vector; and They are and Auxiliary variables, This is the system output, and u is the input. It is an estimate of the unknown ideal weight vector.

2. A processor, characterized in that, The processor is used to run a program, wherein the program executes the unknown nonlinear dynamic approximation method for a lower limb exoskeleton robot as described in claim 1.

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