Functional electrical stimulation control method and system based on distributed NOILC

Abstract

The invention provides a distributed NOILC-based functional electrical stimulation control method and system, and the method comprises the steps: obtaining an angle error of a current period of a target user, and enabling the angle error to be obtained through calculation according to an actual ankle joint angle and a preset reference angle of a previous period of the target user; the angle error is input to a preset distributed NOILC controller, so that the distributed NOILC controller carries out distributed NOILC control of the current period on each subsystem according to the angle error, a NOILC control result of the previous period and a plurality of preset learning parameters, and a NOILC control result of the current period is generated; the NOILC control result of the current period is input to a preset linearization controller, so that the linearization controller generates an electrical stimulation signal sequence of the current period, the stimulation pulse width of each muscle in the functional electrical stimulation process is dynamically adjusted, the gradual convergence of the angle error of the ankle joint is achieved, and the functional electrical stimulation of the ankle joint is achieved. And the accuracy of electrical stimulation signal output in functional electrical stimulation is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electrical signal control, and particularly relates to a functional electrical stimulation control method and system based on a decentralized NOILC. BACKGROUND

[0002] Functional Electrical Stimulation (FES) is a common intervention technique for correcting hemiplegic gait, which produces movement by stimulating the neural tissue that innervates the muscles. In 1961, Liberson et al. first applied FES to increase the dorsiflexion angle during the swing phase. Since then, researchers have developed many FES systems to help stroke patients walk better by correcting foot drop, enhancing propulsion during the stance phase, and improving control of the knee or hip joint. Given the nonlinear and time-varying characteristics of the stimulated muscles, researchers have continuously improved the closed-loop control strategy of the functional electrical stimulator. Some studies adjust the electrical stimulation according to the patient's movement performance, using sensors to capture angle or electromyography (EMG) signals as feedback, and adopting methods such as fuzzy logic control, finite state machine, artificial neural network, and iterative learning control (ILC) to adjust the stimulation input. Specifically, the ILC algorithm has been proven to be able to overcome the convergence limit, provide stable tracking performance, and suppress periodic disturbances at the same time.

[0003] Currently, most research on electrical stimulation focuses on sagittal plane movement, i.e., stimulating lower limb muscles in a predetermined sequence to enhance flexion and extension of the hip, knee, or ankle joints. However, human lower limb joints have multiple degrees of freedom, requiring coordinated activation of multiple muscles to achieve a balanced and natural gait; therefore, the coupling between muscles must be considered. When considering foot movement, it is crucial to consider the cross-coupling between FES parameters and foot orientation angles. Some researchers have placed electrode arrays on branches of the peroneal and tibial nerves to achieve straight foot elevation by identifying the optimal combination of virtual electrodes. However, this identification process is time-consuming and cannot adaptively adjust the virtual electrodes to accommodate changes in muscle dynamics. Seel et al. used two distributed P-type iterative learning controllers to co-activate the tibialis anterior and peroneus longus muscles through nonlinear decoupling. Although this approach enables stroke patients to achieve natural dorsiflexion and eversion of the foot while walking, the empirically set learning gain does not take into account the individual musculoskeletal dynamics of different subjects. Some models or algorithms based on fixed parameters perform poorly when there are significant individual differences among patients, failing to adapt to the physiological characteristics of different patients or changes in muscle response over long-term use, thus affecting the stability and sustainability of control. Furthermore, there is currently a lack of a structurally sound, stable, and closed-loop scheme capable of achieving "feedforward-feedback coordinated control," making it difficult to achieve comprehensive and precise regulation of ankle joint movement. Summary of the Invention

[0004] To address the aforementioned technical problems, this application provides a functional electrical stimulation control method and system based on distributed NOILC, which improves the accuracy of electrical signal release during functional electrical stimulation.

[0005] In a first aspect, embodiments of this application provide a functional electrical stimulation control method based on distributed NOILC, comprising: The angle error of the target user in the current cycle is obtained. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. The angle error is input to a preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. The NOILC control result of the current cycle is input to a preset linearization controller so that the linearization controller generates an electrical stimulation signal sequence for the current cycle. The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

[0006] This application provides a functional electrical stimulation control method based on distributed NOILC. It constructs a personalized musculoskeletal model using historical motion data, adapting to the physiological differences of different patients. This model accurately simulates the nonlinear and dynamic characteristics of the target user's musculoskeletal system, providing a precise mathematical basis for subsequent electrical stimulation control. Then, a linearized controller is constructed to compensate for the nonlinear characteristics of the musculoskeletal dynamics model, improving the accuracy of electrical signal release during functional electrical stimulation. In the specific control strategy, a distributed NOILC control method is employed. In each iteration, the angle error of the current cycle is input to the distributed NOILC controller, enabling it to dynamically adjust the NOILC control results of the previous cycle. Each subsystem corresponds to a specific musculoskeletal model and different learning parameters, ensuring that each subsystem is associated with a single electrically stimulated muscle. Simultaneously, the combined effects of all subsystems are considered, further improving the accuracy of electrical signal release during functional electrical stimulation.

[0007] Furthermore, the distributed NOILC controller performs distributed NOILC control on each subsystem for the current cycle based on the angle error, the NOILC control result of the previous cycle, and several preset learning parameters, generating the NOILC control result for the current cycle, including: The angle compensation value of each subsystem is calculated based on each of the learning parameters and the angle error. Based on the NOILC control results of the previous cycle and the angle compensation values, determine the angle values ​​that each subsystem needs to output in the current cycle; Based on the angle values ​​that each subsystem needs to output in the current cycle, the NOILC control result for the current cycle is generated.

[0008] In this embodiment, the angle compensation value of each subsystem is calculated using various learning parameters, and the output is generated by combining the control results of the previous cycle. This achieves dynamic compensation for angle errors, reduces the impact of accumulated errors on subsequent cycles, and improves the accuracy of electrical signal release during functional electrical stimulation. Simultaneously, the distributed structure allows each subsystem to operate independently, avoiding the resource bottleneck of centralized control and improving real-time computational efficiency during functional electrical stimulation.

[0009] In one possible implementation, the construction of the musculoskeletal dynamics model based on the Hammerstein model and the target user's historical motion data includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

[0010] This application provides a method for constructing a musculoskeletal dynamics model. This method employs a Hammerstein architecture to develop a personalized dual-input, dual-output ankle musculoskeletal model for each target user. Compared to other models, the Hammerstein model can ideally simulate the FES response of muscles under isometric contraction to different electrical stimulation intensities. Since each target user has different musculoskeletal characteristics and varying degrees of neural damage, the personalized Hammerstein model can optimize the electrical stimulation effect and improve the accuracy of electrical signal release during functional electrical stimulation. Furthermore, constructing an initial musculoskeletal dynamics model based on a preset number of initial musculoskeletal models helps identify multi-degree-of-freedom ankle joint movements caused by different muscle activations. This allows the musculoskeletal dynamics model to have a simple structure while maintaining high accuracy, capturing the complex characteristics of muscle kinematics and providing strong support for model predictive control in FES tracking tasks.

[0011] Furthermore, the process of constructing the linearized controller based on the musculoskeletal dynamics model includes: Based on the musculoskeletal dynamics model, the inverse function of the static nonlinear model in each of the musculoskeletal models is calculated; The linearization controller is constructed based on the inverse functions of each of the musculoskeletal models.

[0012] In this application embodiment, a linearized controller is constructed using the inverse function of the musculoskeletal model. The inverse function realizes the linearization of the nonlinear system, reduces the difficulty of controller design, improves the response speed of the electrical stimulation signal in each cycle, and at the same time, the linearization process can effectively reduce the sensitivity of model parameters, avoid control failure caused by muscle dynamic changes, and improve the accuracy of electrical signal release in functional electrical stimulation.

[0013] In one possible implementation, the step of constructing each of the subsystems based on the respective muscle models in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained.

[0014] The embodiments of this application construct a system output model based on a preset time step and the subsystem response process, thereby obtaining each subsystem. The preset time step ensures that the control signals of each subsystem are synchronized with the actual muscle response. At the same time, the system output model is calculated based on the response results of the subsystem at each time step, so that each subsystem captures time-varying characteristics such as muscle fatigue during the construction process, further improving the accuracy of electrical signal release in functional electrical stimulation.

[0015] In one possible implementation, the number of subsystems is two, wherein the first subsystem corresponds to the muscles of the tibialis anterior and the second subsystem corresponds to the muscles of the peroneus longus.

[0016] Furthermore, the subsystem is a single-input dual-output subsystem, the input data of the subsystem is an electrical stimulation signal, and the output data of the subsystem is the pitch angle and roll angle generated by the corresponding muscle after stimulation.

[0017] In this embodiment, the number of subsystems is limited to 2, corresponding to the tibialis anterior and peroneus longus muscles. The input is an electrical stimulation signal, and the output is pitch angle and roll angle. The provided dual-subsystem structure is specifically designed for ankle dorsiflexion and eversion movements, optimizes the coordinated activation of specific muscle groups, and outputs pitch angle and roll angle, taking into account both sagittal and coronal plane motion correction, reducing gait abnormalities of the target user, and further improving the accuracy of electrical signal release in functional electrical stimulation.

[0018] Secondly, correspondingly, embodiments of this application provide a functional electrical stimulation control system based on distributed NOILC, including an acquisition module, a control module, and a signal generation module; The acquisition module is used to acquire the angle error of the target user in the current cycle. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. The control module is used to input the angle error to a preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. The signal generation module is used to input the NOILC control result of the current cycle to a preset linearization controller, so that the linearization controller generates an electrical stimulation signal sequence for the current cycle. The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

[0019] In one possible implementation, the construction of the musculoskeletal dynamics model based on the Hammerstein model and the target user's historical motion data includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

[0020] In one possible implementation, the step of constructing each of the subsystems based on the respective muscle models in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained. Attached Figure Description

[0021] Figure 1 A flowchart illustrating a functional electrical stimulation control method based on distributed NOILC provided in this application embodiment; Figure 2 A schematic diagram of the control process of a functional electrical stimulation control method based on distributed NOILC provided in an embodiment of this application; Figure 3 A schematic diagram of the musculoskeletal kinematic model of the ankle joint in a functional electrical stimulation control method based on distributed NOILC provided in an embodiment of this application; Figure 4 A schematic diagram of the pulse width curve of electrical stimulation released during the process of acquiring historical motion data of a target user; Figure 5 A schematic diagram of the overall closed-loop control system structure of a functional electrical stimulation control method based on distributed NOILC provided for embodiments of this application; Figure 6 This is a schematic diagram of a functional electrical stimulation control system based on distributed NOILC, provided as an embodiment of this application. Detailed Implementation

[0022] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0023] It should be noted that the step numbers in this document are only for the convenience of explaining the specific embodiments and are not intended to limit the order in which the steps are performed. In the description of this application, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of that feature.

[0024] Throughout the manual, NOILC, short for Norm-Optimal Iterative Learning Control, is described as an iterative learning control method based on optimization theory. It aims to progressively optimize the tracking performance of a system in repetitive tasks by minimizing a norm-based objective function that includes the tracking error and control input. Its core idea is to solve for a norm-optimal control law in each iteration, ensuring that the error converges monotonically with the number of iterations and achieving the desired system response while satisfying constraints.

[0025] Example 1: like Figure 1 As shown, Embodiment 1 provides a functional electrical stimulation control method based on distributed NOILC, including steps S1-S3: Step S1: Obtain the angle error of the target user in the current cycle. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. Step S2: Input the angle error to the preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. Step S3: Input the NOILC control result of the current cycle into a preset linearization controller so that the linearization controller generates the electrical stimulation signal sequence of the current cycle; The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

[0026] This application provides a functional electrical stimulation control method based on distributed NOILC. It constructs a personalized musculoskeletal model using historical motion data, adapting to the physiological differences of different patients. This model accurately simulates the nonlinear and dynamic characteristics of the target user's musculoskeletal system, providing a precise mathematical basis for subsequent electrical stimulation control. Then, a linearized controller is constructed to compensate for the nonlinear characteristics of the musculoskeletal dynamics model, improving the accuracy of electrical signal release during functional electrical stimulation. In the specific control strategy, a distributed NOILC control method is employed. In each iteration, the angle error of the current cycle is input to the distributed NOILC controller, enabling it to dynamically adjust the NOILC control results of the previous cycle. Each subsystem corresponds to a specific musculoskeletal model and different learning parameters, ensuring that each subsystem is associated with a single electrically stimulated muscle. Simultaneously, the combined effects of all subsystems are considered, further improving the accuracy of electrical signal release during functional electrical stimulation.

[0027] In the field of functional electrical stimulation (fEP), previous studies have mostly focused on stimulating only the tibialis anterior muscle to correct swing-phase foot drop. However, simply stimulating the tibialis anterior is insufficient to improve ankle joint movement in the coronal plane, especially considering the inversion symptoms often associated with foot drop. A research team at the Technical University of Berlin discovered that simultaneously activating both the tibialis anterior and peroneus longus muscles can effectively address this issue. As the number of muscles involved in stimulation increases, their nonlinear interactions may become more significant. To address this challenge, this application employs a Hammerstein model to develop a personalized dual-input dual-output ankle musculoskeletal model for each subject. Compared to other models, the Hammerstein model ideally simulates the FES response of muscles to different electrical stimulation intensities under isometric contraction. Since each stroke patient has different musculoskeletal characteristics and varying degrees of neurological damage, the personalized Hammerstein model can optimize the effects of electrical stimulation. Furthermore, the dual-input dual-output model structure helps identify multidirectional foot movements caused by activation of different muscles. The results show that the model not only has a simple structure and high accuracy, but also captures the complex characteristics of muscle kinematics and supports automatic parameter estimation, which provides strong support for model predictive control in FES tracking tasks.

[0028] Once the model information is accurately established, the stimulation parameters need to be iteratively adjusted in each cycle to optimize performance. Previous studies have shown that applying the ILC algorithm in FES systems can provide optimal stimulation intensity, promote rapid convergence to the desired target, and help prevent muscle fatigue. However, most of them stimulate single muscles independently without considering the coupling effect when muscles are co-activated. To address this issue, embodiments of this application employ a decentralized control framework. Each subsystem is associated with a single electrically stimulated muscle and is updated using only local model information. In a preferred embodiment, the musculoskeletal dynamics model of the ankle joint includes a musculoskeletal model of the tibialis anterior and a musculoskeletal model of the peroneus longus. Results show that, compared to conventional FES techniques targeting only the tibialis anterior, the method provided in embodiments of this application can effectively balance the stimulation intensity of the tibialis anterior and peroneus longus and exhibits a smaller co-tracking error. Meanwhile, prolonged electrical stimulation can lead to muscle fatigue, and the co-contraction of antagonistic muscles may further accelerate the onset of muscle fatigue. To address this issue, embodiments of this application apply decentralized NOILC to calculate the stimulation envelope for each iteration. Compared to traditional rectangular and trapezoidal stimulation patterns, the electrical stimulation envelope more closely approximates actual muscle activation, helping to slow down muscle fatigue. Furthermore, NOILC helps achieve minimal error and converge to the optimal input, improving the accuracy of electrical signal delivery in functional electrical stimulation.

[0029] In a preferred embodiment, the functional electrical stimulation control process based on distributed NOILC is as follows: Figure 2 As shown, the system mainly includes an ankle musculoskeletal kinematic model, a distributed closed-loop controller, a Dynamic Time Warp (DTW) module, and a kinematic information measurement module (not shown in the figure). The kinematic information measurement module, used to determine the actual tracking position for each cycle, can be composed of a motion capture system and inertial sensors. Due to the delay between stimulus and joint angle response, direct feedback control of joint angles during gait cannot be achieved through FES. Therefore, this embodiment measures the actual ankle joint angle of the previous cycle and aligns it with a standard angle reference band using DTW to calculate the angle error. The standard angle reference range is defined based on measurements from healthy subjects. Then, the adaptive controller uses this angle error and the functional electrical stimulation control method provided in this application to calculate the stimulation signals for the two muscles in subsequent iterations.

[0030] Further, in step S2, the distributed NOILC controller performs distributed NOILC control on each subsystem for the current cycle based on the angle error, the NOILC control result of the previous cycle, and several preset learning parameters, generating the NOILC control result for the current cycle, including: The angle compensation value of each subsystem is calculated based on each of the learning parameters and the angle error. Based on the NOILC control results of the previous cycle and the angle compensation values, determine the angle values ​​that each subsystem needs to output in the current cycle; Based on the angle values ​​that each subsystem needs to output in the current cycle, the NOILC control result for the current cycle is generated.

[0031] In this embodiment, the angle compensation value of each subsystem is calculated using various learning parameters, and the output is generated by combining the control results of the previous cycle. This achieves dynamic compensation for angle errors, reduces the impact of accumulated errors on subsequent cycles, and improves the accuracy of electrical signal release during functional electrical stimulation. Simultaneously, the distributed structure allows each subsystem to operate independently, avoiding the resource bottleneck of centralized control and improving real-time computational efficiency during functional electrical stimulation.

[0032] In one possible implementation, the construction of the musculoskeletal dynamics model based on the Hammerstein model and the target user's historical motion data includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

[0033] This application provides a method for constructing a musculoskeletal dynamics model. This method employs a Hammerstein architecture to develop a personalized dual-input dual-output ankle musculoskeletal model for each target user. Compared to other models, the Hammerstein model can ideally simulate the FES response of muscles under isometric contraction to different electrical stimulation intensities. Since each target user has different musculoskeletal characteristics and varying degrees of nerve damage, the personalized Hammerstein model can optimize the electrical stimulation effect and improve the accuracy of electrical signal release during functional electrical stimulation. Furthermore, constructing an initial musculoskeletal dynamics model based on a preset number of initial musculoskeletal models helps identify multi-directional foot movements caused by different muscle activations. This allows the musculoskeletal dynamics model to have a simple structure while maintaining high accuracy, capturing the complex characteristics of muscle kinematics and providing strong support for model predictive control in FES tracking tasks.

[0034] In a preferred embodiment, such as Figure 3 As shown, the musculoskeletal kinematic model of the ankle joint mainly consists of two parts: the first part is a muscle model with a Hammerstein structure, and the second part is a skeletal model. The Hammerstein model comprises two parts: a static nonlinear recruitment process describing muscle activation characteristics, and a linear dynamic model simulating the muscle's contractile response to electrical stimulation signals. Furthermore, the skeletal dynamics of human limbs can be modeled using Rigid Body Dynamics (RBD) to describe the motion characteristics of the skeletal system under external forces and muscle-driven forces.

[0035] exist Figure 3 In the structure shown, and They represent the tibialis anterior and peroneus longus muscles, respectively. k Represents the number of iterations. This represents a complex variable in the Z-transform. Input It is a non-negative electrical stimulation signal. This represents the nonlinear static recruitment characteristics of muscles. For steady-state isometric muscle torque, For linear contraction dynamics, The torque generated by the muscle, and These represent the total torques acting on the skeletal system in the pitch and roll directions, respectively. and Represents ankle joint skeletal dynamics, output and These are pitch angle and roll angle, respectively.

[0036] The static recruitment characteristics of the Hammerstein model, or so-called isometric recruitment curves (IRCs), represent the relationship between the electrical stimulation signal and the output torque of the corresponding muscle. Because... and These are all nonlinear static recruitment characteristics of the tibialis anterior muscle. The embodiments in this application have appropriately simplified the model structure to optimize the parameter identification process, i.e., assuming... Similarly, suppose Due to the continuous and monotonically increasing properties of IRC, It can be restated in the following general polynomial form: And it must satisfy the condition of increasing monotonicity: in, , , These are the parameters to be identified.

[0037] The overall linear musculoskeletal dynamics model (including linear muscle dynamics and skeletal dynamics) can be modeled as follows: ,in Furthermore, the linear musculoskeletal model can be written as: in, It is a unit delay. and These are the number of poles and zeros, respectively. It is the delay from input to output. , and The values ​​are set to 2, 1, and 1 respectively. and These are parameters that need to be identified.

[0038] In this study, input / output data were used to identify the linear and nonlinear parameters of the Hammerstein model. This process begins with an analysis of the transfer function. and It begins with the initial assumptions, and then identifies the nonlinear parameters. Subsequently, while maintaining Determine separately under fixed conditions and The same method is applied to identify the parameters of the peroneus longus muscle. Constrained optimization solvers can effectively solve both linear and nonlinear parameter identification tasks. Therefore, after constructing an initial musculoskeletal dynamics model with several parameters to be identified, we can determine each parameter to be identified in the initial musculoskeletal dynamics model using a parameter fixing method based on the target user's historical motion data. The specific process is as follows: Surface electrical stimulation electrodes were pre-placed on the tibialis anterior and peroneus longus muscles of the affected side of the target user to precisely control ankle joint movement. During the measurement, the target user sat in a fixed chair with both legs naturally suspended, ensuring that foot movement was entirely driven by electrical stimulation signals and avoiding interference from external forces. Parameter identification of the ankle joint model relied on the input-output dataset [u, y]. The input signal... Sine wave stimulation was used, with pulse widths varying between 0 and 400 µs and normalized to [0, 1] to fit the model calculations. Figure 4 As shown, each sine wave lasts 1.2 seconds, for a total of 7 cycles. To prevent muscle fatigue, a 3.6-second rest period is set between every two waveforms to ensure the target user maintains a stable muscle response during the experiment. Output signal The pitch and roll angles of the foot relative to the ground are represented by the motion capture system. Each parameter recognition process lasts approximately one minute. After the experiment, the collected input-output dataset is used for validation testing to evaluate the accuracy of the model's recognition.

[0039] Furthermore, the process of constructing the linearized controller based on the musculoskeletal dynamics model includes: Based on the musculoskeletal dynamics model, the inverse function of the static nonlinear model in each of the musculoskeletal models is calculated; The linearization controller is constructed based on the inverse functions of each of the musculoskeletal models.

[0040] In this application embodiment, a linearized controller is constructed using the inverse function of the musculoskeletal model. The inverse function realizes the linearization of the nonlinear system, reduces the difficulty of controller design, improves the response speed of the electrical stimulation signal in each cycle, and at the same time, the linearization process can effectively reduce the sensitivity of model parameters, avoid control failure caused by muscle dynamic changes, and improve the accuracy of electrical signal release in functional electrical stimulation.

[0041] In one possible implementation, the step of constructing each of the subsystems based on the respective muscle models in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained.

[0042] The embodiments of this application construct a system output model based on a preset time step and the subsystem response process, thereby obtaining each subsystem. The preset time step ensures that the control signals of each subsystem are synchronized with the actual muscle response. At the same time, the system output model is calculated based on the response results of the subsystem at each time step, so that each subsystem captures time-varying characteristics such as muscle fatigue during the construction process, further improving the accuracy of electrical signal release in functional electrical stimulation.

[0043] In one possible implementation, the number of subsystems is two, wherein the first subsystem corresponds to the muscles of the tibialis anterior and the second subsystem corresponds to the muscles of the peroneus longus.

[0044] Furthermore, the subsystem is a single-input dual-output subsystem, the input data of the subsystem is an electrical stimulation signal, and the output data of the subsystem is the pitch angle and roll angle generated by the corresponding muscle after stimulation.

[0045] In this embodiment, the number of subsystems is limited to 2, corresponding to the tibialis anterior and peroneus longus muscles. The input is an electrical stimulation signal, and the output is pitch angle and roll angle. The provided dual-subsystem structure is specifically designed for ankle dorsiflexion and eversion movements, optimizes the coordinated activation of specific muscle groups, and outputs pitch angle and roll angle, taking into account both sagittal and coronal plane motion correction, reducing gait abnormalities of the target user, and further improving the accuracy of electrical signal release in functional electrical stimulation.

[0046] In a preferred embodiment, the ankle musculoskeletal model is a nonlinear system due to the inherent nonlinearity of its recruitment characteristics. Therefore, this embodiment requires the design of a linearization controller to linearize the system. Based on this, a dual-input, dual-output distributed norm-optimal iterative learning controller is further designed to correct foot drop and inversion symptoms during the swing phase, improving the walking ability of hemiplegic patients. The closed-loop control system structure is as follows: Figure 5 As shown, it includes a distributed NOILC controller, a linearized controller, and a musculoskeletal dynamics model, in which... For reference pitch angle Compared to the actual pitch angle The error between them For reference roll angle Compared with the actual roll angle The error between them. For the learning gain of distributed NOILC, and For controller output. and It is a linearization controller. and This is the calculated pulse width for electrical stimulation.

[0047] Based on the reversible equivalent static recruitment property and In this embodiment, a linearization controller is constructed to compensate for nonlinearity, as shown in the following formula: Each muscle is considered a subsystem, with two single-input, double-output subsystems working together to execute an action of duration. A repeated tracking task for samples. In the k-th iteration, subsystem i is modeled by the system: here Let be the state vector of the subsystem. It is an input to subsystem i, and It includes two outputs from the subsystem. The time step is... . Let be the state transition matrix of the subsystem. The input matrix of the subsystem, Let be the output matrix of the subsystem. At the end of each iteration, subsystem i is reset to its initial conditions. This condition remains constant throughout all iterations.

[0048] The system output in the k-th iteration is the sum of the contributions of all subsystems, that is: in It is a scalar weight. The signal is directly measurable and accessible to all subsystems. As the number of iterations increases, the ankle angle must converge to the desired trajectory. ,Right now: Let each iteration be represented as a single sample of the high-dimensional "lifted" system. Therefore, the signals in (1-5) to (1-7) become hypervectors, i.e.: (1-5) can be rewritten in an equivalent form: in It is the Tollitz matrix: This is along the experimental transfer function. The higher-dimensional implementation involves unfolding the system's response along time to construct a form similar to the one shown above. and , It is an identity matrix. This is a response to the initial conditions: The functional electrical stimulation control method based on distributed NOILC provided in this application aims to correct the pitch and roll angles during the gait swing phase by adaptively adjusting the stimulation signal, thereby achieving gait rehabilitation. This process can be expressed as an optimization problem, where the objective of each iteration is to minimize the cost function. Its mathematical expression is as follows: In each iteration, a decentralized ILC update algorithm is used to generate the NOILC control result for the current period: The linear controller is used to generate updates for each subsystem, which in turn generates the electrical stimulation signal sequence for the current cycle: Here, 𝛾>0 represents the scalar learning gain. These are learning parameters, and It is a symmetric positive semidefinite matrix: in, and .

[0049] Furthermore, to ensure the stability of the functional electrical stimulation control method based on distributed NOILC proposed in this application embodiment during the iteration process, this application embodiment uses the spectral radius method to perform convergence analysis on the distributed NOILC controller and the linearized controller in the method.

[0050] Substituting the linearized controller update law (1-14) and the system output model (1-9) into the error definition, we can obtain the next step error as follows: The overall error evolution formula of the system is obtained by reorganization: remember ,but: To ensure that the systematic error tends to 0, it is only necessary to ensure that the matrix The spectral radius is strictly less than 1, that is: Substituting into (1-15), we get: According to the fundamental theory of linear discrete-time systems, the above equation holds if and only if The following restrictions must be met: The results show that when the scalar learning gain Under certain conditions, the spectral radius of the state matrix of the error iteration system is less than 1, thus ensuring the asymptotic convergence of the error and the overall stability of the system.

[0051] In summary, this application proposes a functional electrical stimulation control method based on distributed NOILC. This method combines advanced control theory and electrical stimulation technology, enabling precise release of electrical signals in each cycle. This application constructs a dual-input, dual-output Hammerstein model to model the ankle musculoskeletal system. This model accurately simulates the nonlinear and dynamic characteristics of the musculoskeletal system, providing a precise mathematical basis for subsequent electrical stimulation control. The Hammerstein model combines the system's inputs (such as stimulation signals) and outputs (such as ankle angle changes), effectively capturing the system's complex behavior and providing a more efficient control strategy. Furthermore, to achieve closed-loop control and progressive correction of ankle angle errors, this application introduces a distributed norm optimal iterative learning controller, i.e., a distributed NOILC controller + a linearized controller. This distributed norm optimal iterative learning controller can dynamically adjust the stimulation pulse widths of the tibialis anterior and peroneus longus muscles based on real-time gait data to achieve progressive convergence of ankle angle errors. Through an iterative learning process, the controller can continuously optimize electrical stimulation parameters in multiple cycles, ensuring the stability and corrective effect of the patient's gait, thereby effectively reducing foot drop and inversion symptoms in hemiplegic patients.

[0052] Example 2: like Figure 6 As shown, Embodiment 2 provides a functional electrical stimulation control system based on distributed NOILC, including an acquisition module 10, a control module 20, and a signal generation module 30; The acquisition module 10 is used to acquire the angle error of the target user in the current cycle. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. The control module 20 is used to input the angle error to a preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. The signal generation module 30 is used to input the NOILC control result of the current cycle to a preset linearization controller, so that the linearization controller generates an electrical stimulation signal sequence for the current cycle. The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

[0053] Furthermore, the distributed NOILC controller performs distributed NOILC control on each subsystem for the current cycle based on the angle error, the NOILC control result of the previous cycle, and several preset learning parameters, generating the NOILC control result for the current cycle, including: The angle compensation value of each subsystem is calculated based on each of the learning parameters and the angle error. Based on the NOILC control results of the previous cycle and the angle compensation values, determine the angle values ​​that each subsystem needs to output in the current cycle; Based on the angle values ​​that each subsystem needs to output in the current cycle, the NOILC control result for the current cycle is generated.

[0054] In one possible implementation, the construction of the musculoskeletal dynamics model based on the Hammerstein model and the target user's historical motion data includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

[0055] Furthermore, the process of constructing the linearized controller based on the musculoskeletal dynamics model includes: Based on the musculoskeletal dynamics model, the inverse function of the static nonlinear model in each of the musculoskeletal models is calculated; The linearization controller is constructed based on the inverse functions of each of the musculoskeletal models.

[0056] In one possible implementation, the step of constructing each of the subsystems based on the respective muscle models in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained.

[0057] In one possible implementation, the number of subsystems is two, wherein the first subsystem corresponds to the muscles of the tibialis anterior and the second subsystem corresponds to the muscles of the peroneus longus.

[0058] Furthermore, the subsystem is a single-input dual-output subsystem, the input data of the subsystem is an electrical stimulation signal, and the output data of the subsystem is the pitch angle and roll angle generated by the corresponding muscle after stimulation.

[0059] This application provides a functional electrical stimulation control system based on distributed NOILC. It constructs a personalized musculoskeletal model using historical motion data, adapting to the physiological differences of different patients. This accurately simulates the nonlinear and dynamic characteristics of the target user's musculoskeletal system, providing a precise mathematical basis for subsequent electrical stimulation control. Then, a linearized controller is constructed to compensate for the nonlinear characteristics of the musculoskeletal dynamics model, improving the accuracy of electrical signal release during functional electrical stimulation. In the specific control strategy, a distributed NOILC control method is adopted. In each iteration, the angle error of the current cycle is input to the distributed NOILC controller, enabling it to dynamically adjust the NOILC control results of the previous cycle. Each subsystem corresponds to a specific musculoskeletal model and different learning parameters, ensuring that each subsystem is associated with a single electrically stimulated muscle. Simultaneously, the combined effects of all subsystems are considered, further improving the accuracy of electrical signal release during functional electrical stimulation.

[0060] For a more detailed explanation of the working principle and procedures of this embodiment, please refer to the relevant description in Embodiment 1.

[0061] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. In particular, it should be noted that any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application for those skilled in the art.

Claims

1. A functional electrical stimulation control method based on distributed NOILC, characterized in that, include: The angle error of the target user in the current cycle is obtained. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. The angle error is input to a preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. The NOILC control result of the current cycle is input to a preset linearization controller so that the linearization controller generates an electrical stimulation signal sequence for the current cycle. The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

2. The functional electrical stimulation control method based on distributed NOILC as described in claim 1, characterized in that, The distributed NOILC controller performs distributed NOILC control on each subsystem for the current cycle based on the angle error, the NOILC control result of the previous cycle, and several preset learning parameters, generating the NOILC control result for the current cycle, including: The angle compensation value of each subsystem is calculated based on each of the learning parameters and the angle error. Based on the NOILC control results of the previous cycle and the angle compensation values, determine the angle values ​​that each subsystem needs to output in the current cycle; Based on the angle values ​​that each subsystem needs to output in the current cycle, the NOILC control result for the current cycle is generated.

3. The functional electrical stimulation control method based on distributed NOILC as described in claim 1, characterized in that, The musculoskeletal dynamics model, constructed based on the Hammerstein model and the target user's historical motion data, includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

4. The functional electrical stimulation control method based on distributed NOILC as described in claim 1, characterized in that, The linearized controller, constructed based on the musculoskeletal dynamics model, includes: Based on the musculoskeletal dynamics model, the inverse function of the static nonlinear model in each of the musculoskeletal models is calculated; The linearization controller is constructed based on the inverse functions of each of the musculoskeletal models.

5. The functional electrical stimulation control method based on distributed NOILC as described in claim 1, characterized in that, The process of constructing each subsystem based on each muscle model in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained.

6. A functional electrical stimulation control method based on distributed NOILC as described in any one of claims 1-5, characterized in that, The number of subsystems is 2, wherein the first subsystem corresponds to the muscles of the tibialis anterior muscle, and the second subsystem corresponds to the muscles of the peroneus longus muscle.

7. The functional electrical stimulation control method based on distributed NOILC as described in claim 6, characterized in that, The subsystem is a single-input dual-output subsystem. The input data of the subsystem is an electrical stimulation signal, and the output data of the subsystem is the pitch angle and roll angle generated by the corresponding muscle after stimulation.

8. A functional electrical stimulation control system based on distributed NOILC, characterized in that, It includes an acquisition module, a control module, and a signal generation module; The acquisition module is used to acquire the angle error of the target user in the current cycle. The angle error is calculated based on the actual ankle angle of the target user in the previous cycle and the preset reference angle. The control module is used to input the angle error to a preset distributed NOILC controller, so that the distributed NOILC controller performs distributed NOILC control on each subsystem in the current cycle according to the angle error, the NOILC control result of the previous cycle and a number of preset learning parameters, and generates the NOILC control result of the current cycle. The signal generation module is used to input the NOILC control result of the current cycle to a preset linearization controller, so that the linearization controller generates an electrical stimulation signal sequence for the current cycle. The linearization controller is constructed based on the musculoskeletal dynamics model of the ankle joint. The musculoskeletal dynamics model is constructed based on the Hammerstein model and the historical motion data of the target user. The NOILC controller includes various subsystems, each of which is constructed based on a musculoskeletal model in the musculoskeletal dynamics model and corresponds one-to-one with each of the learning parameters. Each learning parameter is calculated based on the internal parameters of each musculoskeletal model.

9. A functional electrical stimulation control system based on distributed NOILC as described in claim 1, characterized in that, The musculoskeletal dynamics model, constructed based on the Hammerstein model and the target user's historical motion data, includes: Based on the process of muscle contraction response to electrical stimulation signals, a static nonlinear model and a dynamic linear model with several parameters to be identified are constructed as the initial muscle model. Based on rigid body dynamics and the motion characteristics of the skeletal system under the action of external forces and muscle driving forces, an initial skeletal model with several parameters to be identified is constructed. By combining the initial muscle model and the initial bone model, an initial muscle-skeleton model is constructed; Based on a preset number of initial musculoskeletal models, construct an initial musculoskeletal dynamics model; Based on the target user's historical motion data, the parameters to be identified in the initial musculoskeletal dynamics model are determined by the parameter fixing method, thereby obtaining the musculoskeletal dynamics model.

10. A functional electrical stimulation control system based on distributed NOILC as described in claim 1, characterized in that, The process of constructing each subsystem based on each muscle model in the musculoskeletal dynamics model includes: Based on the internal parameters of each musculoskeletal model, the state transition matrix, input matrix, and output matrix of each subsystem are determined, and then each initial subsystem is constructed. Obtain the preset time step of the NOILC controller in each iteration; The historical motion data of the target user is input into each of the initial subsystems, and the response results of each subsystem to the input data are obtained at each time step; Based on the preset time step, the state transition matrix, input matrix, output matrix of each subsystem, and each response result, the system output model of each subsystem is calculated, and thus each subsystem is obtained.

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