Numerical simulation method of human body-balance plate control system model

Abstract

The invention discloses a numerical simulation method of a human body-balance plate control system model. The method comprises the following steps: establishing a human body and balance plate coupled dynamic model for numerical simulation; the model is specifically a sagittal plane model in which a human body stands on the balance plate, the feet are coupled with the balance plate, the rest parts are composed of shanks, thighs and an upper body, and the whole body is formed by connecting ankles, knees and hip joints; the balance plate is connected with the ground through a revolute pair, the joint has adjustable rotational rigidity, and a method for simulating an unstable ground or an unstable external environment is provided; the control moments at the joints take into account neural sense feedback, such as proprioceptive, vestibular and visual feedback, and neural response delays that affect the balance of the human body. The human body-balance plate model is established by considering nerve sense feedback, multiple joints and external environment influence and is used for numerical simulation, and a model and a numerical simulation method conforming to a real human body balance mode are provided for research of human body stability.

Description

Technical Field

[0001] The invention relates to the fields of mechanical multi-body dynamics and biomedicine, and in particular to a numerical simulation method of a human body-balance board control system model. Background Art

[0002] At present, most studies use ankle joint models or ankle-hip joint models to simulate human balance in the sagittal plane. The ankle-hip joint model uses a secondary inverted pendulum to represent the human body in the sagittal plane, assuming that the swing of the body is controlled only by muscles attached to the ankle and hip joints, while ignoring the important role of the knee joint in balance. Although the ankle-hip joint model can reflect the balance of the human body to a certain extent, it is not enough to accurately simulate the balance ability of humans in the face of complex interference, especially in scenarios where the influence of the knee joint on balance needs to be considered.

[0003] In practical applications, many medical devices with balance boards are used for human stability training and testing. These devices usually place individuals on a balance board for training, which is defined as a rotating surface with adjustable stiffness that can rotate around a pivot. The balance board provides a simple way to simulate external perturbations and unstable environments. Although some studies have incorporated the balance board into the human body model for stability analysis, no study has yet considered the dynamic interaction of the ankle, knee, and hip joint models with the balance board.

[0004] The stability of human standing is a complex process involving the coordination of vision, vestibule, proprioception and muscle system. These neural feedback gains have an important influence on the active torque of the joints, which determines the size of the active torque required for the joints to maintain balance. At the same time, the process of the central nervous system integrating neural information to generate control torque is always accompanied by a time delay of neuromuscular response, which is also a factor that cannot be ignored in the analysis of human balance.

[0005] Existing studies on human models have failed to simultaneously consider the combination of ankle, knee, and hip joints, the balance board with adjustable stiffness, and the effects of multiple neural feedback and time delays. There is a lack of a more comprehensive model that conforms to the real human movement pattern for numerical simulation analysis. This suggests that a numerical simulation method for the human-balance board control system model should be developed. This will provide a theoretical basis and guidance for a deeper understanding of the human balance mechanism and for improving sports training and rehabilitation programs. Summary of the invention

[0006] In view of the above technical problems, the purpose of the present invention is to provide a numerical simulation method for a human-balance board control system model. To provide a more comprehensive model that conforms to the real human movement mode for the study of human stability analysis for numerical simulation analysis. To achieve the above purpose, the present invention adopts the following technical solution to achieve it.

[0007] A numerical simulation method for a human body-balance board control system model, the steps are as follows:

[0008] Step 1, based on the human body-balance board system and combined with the Lagrangian principle, a human body-balance board dynamics model is established;

[0009] Step 2, based on the human body-balance board dynamics model, a torsional moment model at the pivot of the balance board is established, wherein the torsional stiffness and time lag are adjustable to simulate an unstable ground or external environment;

[0010] Step 3, based on the human body-balance board dynamics model, establish the passive torque model at the ankle, knee and hip joints, and the magnitude of the passive torque is determined by the inherent passive damping and stiffness of the joints;

[0011] Step 4, based on the human-balance board dynamics model, establish the active control torque model at the ankle, knee and hip joints. The magnitude of the active control torque is determined by proprioception, vestibular sensation, visual feedback gain and reaction time delay factors;

[0012] Step 5, combining the human body-balance board dynamics model with all joint control torque models to form a human body-balance board control system model;

[0013] Step 6, input the model of the human body-balance board control system into mathematical modeling software, and use the software to perform numerical simulation analysis on the model.

[0014] Compared with the prior art, the present invention has the following significant advantages:

[0015] (1) Considering the dynamic interaction of ankle, knee, and hip joints: The ankle joint model or ankle-hip joint model in the prior art usually ignores the important role of other joints in balance. The present invention can more accurately simulate the complex dynamic behavior of the human body in sagittal plane balance through the dynamic interaction of multiple joints at the same time.

[0016] (2) Introducing a balance board with adjustable stiffness and time lag: In the present invention, the dynamic interaction of the balance board is incorporated into the model, so that the simulation can more realistically simulate the influence of the external environment and the dynamic changes in balance ability detection training.

[0017] (3) Considering the influence of multiple neural sensory feedback and time delay: The present invention introduces these physiological factors (such as visual, vestibular, proprioceptive and other neural sensory feedback and the time delay of neuromuscular response) into the model, making the model more consistent with the actual human balance control.

[0018] (4) A more comprehensive and realistic model: The numerical simulation method proposed in the present invention integrates the biomechanical interaction of joints, the physical properties of the balance board, neural feedback and its time delay, and can simulate the dynamic process of human balance more comprehensively and accurately, thereby providing strong theoretical support and guidance for in-depth research on the human balance mechanism and optimizing sports training and rehabilitation programs. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 A sagittal view of the human body-balance board provided by the present invention.

[0020] Figure 2 A schematic flow chart of the numerical simulation method provided by the present invention.

[0021] Figure 3 The motion result diagram of the human body-balance board model under the first set of parameter conditions provided by the embodiment of the present invention:

[0022] Among them, (a) is the solution trajectory of the angular displacement of the ankle, knee and hip joints with respect to time, and (b)-(d) are the phase plane diagrams of the motion of each joint.

[0023] Figure 4 The motion result diagram of the human body-balance board model under the second set of parameter conditions provided by the embodiment of the present invention:

[0024] Among them, (a) is the solution trajectory of the angular displacement of the ankle, knee and hip joints with respect to time, and the red “×” in (b)-(d) is the coordinates of the initial angular displacement and velocity of each joint in the phase plane. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application.

[0026] The values ​​of the physical parameters selected by the model in this embodiment are selected to demonstrate the simulation calculation. When using the model, the parameter values ​​can be selected according to the specific situation or different human bodies in practice. Obviously, the described embodiments are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application.

[0027] The following is combined with Figure 1 to Figure 4 The embodiments of the present invention are described in further detail.

[0028] This embodiment provides a numerical simulation method for a human body-balance board control system model, and the specific steps are as follows:

[0029] Step 1: Based on the human body-balance board system and combined with the Lagrangian principle, a human body-balance board dynamics model is established.

[0030] S1.1, the model is a sagittal plane model of a human body standing on a balance board. The model is specifically a sagittal plane model of a human body standing on a balance board, wherein the foot is coupled to the balance board, and the rest of the body consists of three parts: the calf, the thigh, and the upper body, and the whole is connected by the ankle, knee, and hip joints; the balance board is connected to the ground by a revolute pair, and the connection has an adjustable passive rotation stiffness, and the balance board provides a way to simulate an unstable ground or an unstable external environment; the control torque at each joint of the model takes into account the neural feedback that affects the balance of the human body, such as proprioception, vestibular sensation, and visual feedback, as well as neural reaction time delay.

[0031] like Figure 1 As shown in the figure, the basic structure of the model is divided into several important parts, including the balance board, calf, thigh and upper body, and each part is regarded as a rigid body.

[0032] The physical parameters of the human body model are selected, such as the mass, length, moment of inertia of each body part, etc. The physical parameters of a human body with a weight of 70 kg and a height of 180 cm are selected with reference to GB / T17245-2004 "National Standard for Inertial Parameters of Chinese Adults" and GB / T 10000-2023 "Human Body Dimensions of Chinese Adults". The detailed values ​​and specific meanings are shown in Table 1. Among them, I1, I2 and I3 specifically mean the moment of inertia of each body segment around the coronal axis through its center of mass.

[0033] Table Physical parameters of a 170 kg and 180 cm human body

[0034]

[0035]

[0036] S1.2, the human body-balance board model is modeled with the pivot of the balance board as the origin of the absolute coordinate system. The rotation angles of the balance board, ankle joint, knee joint and hip joint are represented as q0, q1, q2 and q3, respectively. Figure 1 As shown. Then the coordinates of the center of mass of the balance board and the feet, calves, thighs and upper body are x0, y0 (x1, y1) (x2, y2) and (x3, y3), respectively, as follows:

[0037]

[0038] The Lagrangian function value L of the human body-balance board system is expressed as:

[0039] L=TV,

[0040]

[0041] Among them, T is the kinetic energy of the system, V is the potential energy of the system, and the joint angle sequence i = 0, 1, 2, 3.

[0042] S1.3, according to the Euler-Lagrange kinetic equation:

[0043]

[0044] It can be decomposed into:

[0045]

[0046] Among them, q k are the independent generalized coordinates of the particle system, Q k The first derivative of k The main driving force corresponds to q k is the generalized force, and t is the time.

[0047] The dynamic model of the human body-balance board system is obtained as follows:

[0048]

[0049] Among them, q(t), and They represent the angular displacement, angular velocity and angular acceleration vector of each joint respectively.

[0050] M=[M b M1 M2 M3] T is the joint torque vector, where each term represents the torque at the balance board pivot, ankle joint, knee joint and hip joint. D(·) is the inertia matrix, C(·) is the Coriolis term, and G(·) is the gravity term, and their expressions are:

[0051]

[0052] Among them, D 11 ~D 44 are the elements of the inertia matrix D(q), C1~C4 are the Coriolis matrices G1~G4 are the elements of the gravity matrix G(q).

[0053] The specific expression of inertia matrix D(q) is:

[0054]

[0055] D 12 =D 21 =I1+I2+I3+L1 2 m2+L1 2 m3+L2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> m3+m1r1<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +m2r2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +L0m3r3 cos(q1+q2+q3)<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0056] <h2 style=";text-align:left;direction:ltr"> +L0(L2m3+m2r2)cos(q1+q2)+2L1m3r3 cos(q2+q3)+L0(L1m2+L1m3+m1r1)cos(q1)<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0057] <h2 style=";text-align:left;direction:ltr"> +2L1(L2m3+m2r2)cos(q2)+2L2m3r3cos(q3),<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0059] <h2 style=";text-align:left;direction:ltr"> D<h2 style=";text-align:left;direction:ltr"> 13 <h2 style=";text-align:left;direction:ltr"> =D<h2 style=";text-align:left;direction:ltr"> 31 <h2 style=";text-align:left;direction:ltr"> =I2+I3+L2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> m3+m2r2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +L0(L2m3+m2r2)cos(q1+q2)+L1m3r3 cos(q2+q3)<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0060] <h2 style=";text-align:left;direction:ltr"> +L1(L2m3+m2r2)cos(q2)+2L2m3r3 cos(q3)+L0m3r3 cos(q1+q2+q3),<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0062] <h2 style=";text-align:left;direction:ltr"> D<h2 style=";text-align:left;direction:ltr"> 14 <h2 style=";text-align:left;direction:ltr"> =D<h2 style=";text-align:left;direction:ltr"> 41 <h2 style=";text-align:left;direction:ltr"> =I3+m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +L1m3r3cos(q2+q3)+L2m3r3cos(q3)+L0m3r3cos(q1+q2+q3),<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0063] <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0064] <h2 style=";text-align:left;direction:ltr"> D<h2 style=";text-align:left;direction:ltr"> 24 <h2 style=";text-align:left;direction:ltr"> =D<h2 style=";text-align:left;direction:ltr"> 42 <h2 style=";text-align:left;direction:ltr"> =I3+m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +L1m3r3cos(q2+q3)+L2m3r3cos(q3),D<h2 style=";text-align:left;direction:ltr"> 33 <h2 style=";text-align:left;direction:ltr"> =I2+I3+m2r2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +m3L2<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2m3L2r3 cos(q3),<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0065] <h2 style=";text-align:left;direction:ltr"> D<h2 style=";text-align:left;direction:ltr"> 34 <h2 style=";text-align:left;direction:ltr"> =D<h2 style=";text-align:left;direction:ltr"> 43 <h2 style=";text-align:left;direction:ltr"> =I3+m3r3<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +L2m3r3 cos(q3),<h2 style=";text-align:left;direction:ltr"> <h2 style=";text-align:left;direction:ltr">

[0066] <h2 style=";text-align:left;direction:ltr"> D44 =I3+m3r3 2 .

[0067] Coriolis force matrix The specific expression is:

[0068]

[0069] The specific expression of the gravity matrix G(q) is:

[0070]

[0071] G3=-g(m3L2+m2r2)sin(q0+q1+q2)-gm3r3sin(q0+q1+q2+q3),

[0072] G4=-gm3r3sin(q0+q1+q2+q3).

[0073] Step 2, based on the human body-balance board dynamics model, establish a torsional moment model at the pivot of the balance board, whose torsional stiffness and time lag are adjustable to simulate an unstable ground or external environment.

[0074] S2.1 In the human-balance board model, the balance board is coupled to the foot with a concentrated mass. The line connecting the ankle joint and the ground hinge of the balance board should be perpendicular to the plane of the balance board.

[0075] S2.2, the hinge where the balance board is connected to the ground has a torsion spring with adjustable stiffness, and the torsion torque also includes a time delay to simulate the effect of an unstable ground or environment on human balance. The torsion torque model at the pivot of the balance board is:

[0076] M b =K b q0(t-τ b )

[0077] Among them, M b Indicates the torque of the torsion spring on the balance plate, K b is the torsion spring stiffness, q0 is the balance plate rotation angle, τ b is the time delay of the feedback torque of the balancing plate.

[0078] Step 3, based on the human body-balance board dynamics model, establish the passive torque model at the ankle, knee and hip joints. The magnitude of the passive torque is determined by the inherent passive damping and stiffness of the joints.

[0079] S3.1 The torque generated at the ankle, knee and hip joints in the human-balance board model consists of active torque and passive torque, which can be expressed as:

[0080] M1=M1,passive +M 1,active

[0081] M2=M 2,passive +M 2,active

[0082] M3=M 3,passive +M 3,active

[0083] Among them, M i,active is the active torque at each joint, M i,passive is the passive torque at each joint, i=1,2,3.

[0084] S3.2 Passive torque originates from inherent muscle stiffness and damping and acts rapidly as a response to changes in joint angles. Therefore, the passive torque model at the ankle, knee, and hip joints is an instantaneous nonlinear proportional derivative controller expressed as:

[0085]

[0086] Where K ma , K mk and K mh Represents the passive muscle stiffness at the ankle, knee, and hip joints, respectively. ma , C mk and C mh Represent the passive viscous damping coefficients of the muscles at the ankle, knee, and hip joints, respectively. β is a dimensionless parameter that represents the nonlinear relationship between the force and extension of the muscles involved in posture control.

[0087] Step 4, based on the human-balance board dynamics model, establish the active control torque model at the ankle, knee and hip joints. The size of the active control torque is determined by the proprioception, vestibular sense and visual feedback gain and the reaction time delay factor.

[0088] S4.1 When the human body is controlling its balance, it takes time for the neuromuscular system to receive and process sensory signals, and it also takes time for muscles to contract. The effect of time delay on active control torque should be considered here.

[0089] S4.2 The active control torque at the ankle, knee and hip joints in the human-balance board model also needs to consider the neural feedback gain that affects human balance, including proprioception, vestibular and visual feedback gain. Among them, the proprioception system perceives the relative position information between various parts of the body, so it provides joint angle information in the local reference system, while the vestibular and visual systems can perceive the positional relationship between the body and the external environment, so it provides angle information of various parts of the body in the absolute reference system.

[0090] S4.3 According to the influencing factors of active torque, the active control torque model at the ankle joint, knee joint and hip joint is a time-delay proportional controller, which is expressed as:

[0091] M 1,active =K pa q1(t-τ1)+K va (q0(t-τ1)+q1(t-τ1))

[0092] M 2,active =K pk q2(t-τ2)+K vk (q0(t-τ2)+q1(t-τ2)+q2(t-τ2))

[0093] M 3,active =K ph q3(t-τ3)+K vh (q0(t-τ3)+q1(t-τ3)+q2(t-τ3)+q3(t-τ3))

[0094] Where K pa , K pk and K ph K represents the proprioceptive gain at the ankle, knee, and hip joints, respectively. va , K vk and K vh The visual-vestibular joint feedback gains of the ankle, knee and hip joints are represented by τ1, τ2 and τ3, respectively, which represent the reaction lags of the torque generated at the ankle, knee and hip joints.

[0095] Step 5, combining the human body-balance board dynamics model with all joint control torque models to form a human body-balance board control system model.

[0096] The human body-balance board control system model is formed by combining the human body-balance board dynamics model with the joint torque models. Substituting the ankle, knee and hip joint torques and the balance board torque models into the human body-balance board dynamics model, the human body-balance board control system model is:

[0097]

[0098] Step 6, input the model of the human body-balance board control system into mathematical modeling software, and use the software to perform numerical simulation analysis on the model.

[0099] The model has a parameter vector η with unknown values ​​= [K b ,K pa ,K pk ,K ph ,K va ,K vk ,K vh ,Kma ,K mk ,K mh ,C ma ,C mk ,C mh ] and time lag τ=[τ b ,τ1,τ2,τ3]. In order to consider the correlation between the control parameters and reduce the number of parameters to simplify the model, it is necessary to refer to some assumptions in human balance biomechanics.

[0100] First, since the cross-sectional area of ​​the muscles attached to the hip and knee joints is larger than that of the muscles attached to the ankle joint, it is assumed that the muscle stiffness of the hip and knee joints that produces torque is 20% and 10% larger than that of the ankle joint, respectively, that is, K ph =1.2K pa ,K vh =1.2K va ,K pk =1.1K pa ,K vk =1.1K va .

[0101] Second, for the purpose of normalization, we first define K cr = mgh, which means the critical ankle joint stiffness required for the human body to remain stable on a rigid ground when the human body is regarded as a rigid single-degree-of-freedom ankle joint model, where m is the total mass of the calf, thigh and upper body, g is the acceleration of gravity, and h is the distance from the center of mass of the calf, thigh and upper body to the ankle joint. The ratio is defined later and The ratio of the muscle stiffness representing the active control torque to the critical muscle stiffness, i.e., the relative stiffness, is and is dimensionless. Therefore, after simplification, the variable K that affects the active control torque in the system is pa ,K pk ,K ph ,K va ,K vk ,K vh Only by and Similarly, the relative stiffness of the balancing plate in torsional moment is defined as

[0102] For K ma ,K mk ,K mh ,C ma ,C mk ,C mh These control muscles passive torque invariant intrinsic parameters, refer to the actual human body muscle passive parameters estimation, set the parameter value K ma =0.6Kcr ,K mk =0.6K cr ,K mh =0.6K cr ,C ma =0.2K cr ,C mk =0.3K cr ,C mh =0.4K cr .

[0103] For the parameters that need to be studied in the model and time lag τ=[τ b ,τ1,τ2,τ3], and the specific parameter values ​​can be set according to the research objectives.

[0104] The control system model of the human body-balance board was numerically simulated in the MATLAB environment to observe the movement and stability of various parts of the body under different neural feedback gains and time lags. The setting conditions were that the initial angular displacement and angular velocity of the system were set to q(0) = [-0.1-0.1-0.1-0.1] in all cases. T rad and

[0105] Select any of the following two sets of parameters to perform numerical simulation on the model. The motion results are as follows: Figures 3-4 shown.

[0106] 1. Select τ=[τ b ,τ1,τ2,τ3]=[1,10,10,10]ms, the result is as follows Figure 3 shown.

[0107] 2. Select τ=[τ b ,τ1,τ2,τ3]=[1,50,50,50]ms, the result is as follows Figure 4 shown.

Claims

1. A numerical simulation method for a human body-balance board control system model, characterized in that: The method comprises: Step 1, based on the human body-balance board system and combined with the Lagrangian principle, a human body-balance board dynamics model is established; Step 2, based on the human body-balance board dynamics model, a torsional moment model at the pivot of the balance board is established, wherein the torsional stiffness and time lag are adjustable to simulate an unstable ground or external environment; Step 3, based on the human body-balance board dynamics model, establish the passive torque model at the ankle, knee and hip joints, and the magnitude of the passive torque is determined by the inherent passive damping and stiffness of the joints; Step 4, based on the human-balance board dynamics model, establish the active control torque model at the ankle, knee and hip joints. The magnitude of the active control torque is determined by proprioception, vestibular sensation, visual feedback gain and reaction time delay factors; Step 5, combining the human body-balance board dynamics model with all joint control torque models to form a human body-balance board control system model; Step 6, input the model of the human body-balance board control system into mathematical modeling software, and use the software to perform numerical simulation analysis on the model.

2. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: In step 1, a dynamic model of the human body-balance board system is established as follows: S1.

1. The human-balance board dynamic model is a sagittal plane model of a human body standing on a balance board. The basic structure of the model includes the balance board, calf, thigh and upper body, and each part is regarded as a rigid body. S1.

2. The Lagrangian function value L of the human body-balance board system is expressed as: L=TV, Where T is the kinetic energy of the system and V is the potential energy of the system; S1.3, according to the Euler-Lagrange kinetic equation: Among them, q k are the independent generalized coordinates of the particle system, Q k The first derivative of k The main driving force corresponds to q k The generalized force, t is the time; The dynamic model of the human body-balance board system is obtained as follows: Among them, the rotation matrix q(t) = [q0 q1 q2 q3] T The elements in correspond to the rotation angles of the balance board, ankle joint, knee joint, and hip joint respectively; and Represent the angular velocity and angular acceleration vectors of each joint respectively; the torque matrix M=[M b M1M2M3] T The elements in correspond to the torques at the ground hinge, ankle joint, knee joint, and hip joint of the balance board, respectively; D(·) is the inertia matrix, C(·) is the Coriolis term, and G(·) is the gravity term.

3. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: Step 2 contains the following steps: S2.

1. In the human-balance board model, the balance board and the foot are coupled to form a concentrated mass; the line connecting the ankle joint and the ground hinge of the balance board should be perpendicular to the plane of the balance board; S2.

2. The pivot where the balance board is connected to the ground has a torsion spring with adjustable stiffness and time delay to simulate the effect of an unstable ground or environment on human balance. The torsion torque model at the pivot of the balance board is: M b =K b q0(t-τ b ) Among them, M b Indicates the torque of the torsion spring on the balance plate, K b is the torsion spring stiffness, q0 is the rotation angle of the balance plate, τ b is the time delay of the feedback torque of the balancing plate.

4. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: Step 3 contains the following steps: S3.

1. The torque generated at the ankle, knee and hip joints in the human-balance board model consists of active torque and passive torque, which are expressed as: M1=M 1,passive +M 1,active M2=M 2,passive +M 2,active , M3=M 3,passive +M 3,active Among them, M i,active is the active torque, M i,passive is the passive torque, i=1,2,3; S3.2 Passive torque originates from inherent muscle stiffness and damping and acts rapidly as a response to changes in joint angles. Therefore, the passive torque model at the ankle, knee, and hip joints is an instantaneous nonlinear proportional derivative controller, expressed as: Where K ma , K mk and K mh Represents the passive muscle stiffness at the ankle, knee and hip joints respectively; C ma , C mk , and C mh represent the passive viscous damping coefficients of muscles at the ankle, knee, and hip joints, respectively; β is a dimensionless parameter that represents the nonlinear relationship between the force and contraction of the muscles involved in posture control.

5. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: Step 4 includes the following steps: S4.

1. When the human body is controlling its balance, it takes time for the neuromuscular system to receive and process sensory signals, and it also takes time for muscles to contract. Therefore, the active control torque of the joints in the human-balance board dynamics model should take into account the influence of time delay. S4.

2. The active control torque at the ankle, knee and hip joints in the human-balance board model also needs to consider the neural feedback gain that affects human balance, including proprioception, vestibular and visual feedback gain; among them, the proprioception system perceives the relative position information between various parts of the body, so it provides joint angle information in the local reference system, while the vestibular and visual systems can perceive the positional relationship between the body and the external environment, so it provides angle information of various parts of the body in the absolute reference system; S4.

3. According to the influencing factors of active torque, the active control torque model at the ankle joint, knee joint and hip joint is a time-delay proportional controller, which is expressed as M 1,active =K pa q1(t-τ1)+K va (q1(t-τ1)) M 2,active =K pk q2(t-τ2)+K vk (q1(t-τ2)+q2(t-τ2)) M 3,active =K ph q3(t-τ3)+K vh (q1(t-τ3)+q2(t-τ3)+q3(t-τ3)), Where K pa , K pk and K ph represents the proprioceptive feedback gain at the ankle, knee and hip joints respectively; K va , K vk and K vh Represent the visual-vestibular combined feedback gains of the ankle, knee and hip joints respectively; the reaction time delays of generating torque at the ankle, knee and hip joints are represented by τ1, τ2 and τ3 respectively.

6. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: Step 5 includes the following steps: The human body-balance board control system model is formed by combining the human body-balance board dynamics model with the joint torque models. Substituting the ankle, knee and hip joint torques and the balance board torque models into the human body-balance board dynamics model, the human body-balance board control system model is:

7. The numerical simulation method of the human body-balance board control system model according to claim 1, characterized in that: Step 6 contains the following steps: Input the human body-balance board control system model into mathematical modeling software. According to the research objectives and objects, all the physical parameter values ​​of the model can be determined by yourself, and then the software can be used to perform numerical simulation analysis on the control system model.

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