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

Abstract

The application discloses a numerical simulation method of a human body-balance plate control system model, establishes a dynamic model of human body and balance plate coupling and is used for numerical simulation; the model is specifically a sagittal plane model of the human body standing on the balance plate, wherein the foot is coupled with the balance plate, the rest is composed of a lower leg, a thigh and an upper body, and the whole is connected by ankle, knee and hip joints; the balance plate is connected with the ground by a rotary pair, the connecting position is provided with adjustable rotary stiffness, and a method for simulating uneven ground or unstable external environment is provided; the control torque at each joint considers the neural sensation feedbacks, such as proprioception, vestibular sensation and visual feedback, and neural reaction delay, which affect the balance of the human body. The human body-balance plate model is established by considering the neural sensation feedback, multiple joints and external environment influence and is used for numerical simulation, so that a model and a numerical simulation method conforming to the balance mode of the real human body are provided for the research on the stability of the human body.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of mechanical multi-body dynamics and biomedical engineering, and particularly to a numerical simulation method of a human-body- balance-board control system model. BACKGROUND

[0002] Most current researches use ankle joint models or ankle-hip joint models to simulate human body balance in the sagittal plane. The ankle-hip joint model represents the human body in the sagittal plane using a two-link inverted pendulum, assuming that the body swing is controlled only by the 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 some extent, it is not sufficient to accurately simulate the balance ability of humans in the face of complex disturbances, 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 body stability training and detection. 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 disturbances and unstable environments. Although some researches have incorporated the factors of balance boards into human body models for stability analysis, there is currently no research that considers the dynamic interaction of ankle, knee, and hip joint models with balance boards.

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

[0005] Existing researches on human body models have not considered the combination of ankle, knee, and hip joints, adjustable stiffness balance boards, and the influence of multiple neural sensory 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 indicates the need to develop a numerical simulation method of a human-body-balance-board control system model. This will provide a theoretical basis and guidance for a deeper understanding of human balance mechanisms and improved exercise training and rehabilitation programs. SUMMARY

[0006] To solve the above technical problems, the present application provides a numerical simulation method of a human-body-balance-board control system model. A more comprehensive model that conforms to the real human movement pattern is provided for numerical simulation analysis of human stability analysis research. To achieve the above purpose, the present application adopts the following technical solutions.

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

[0008] Step 1, based on the human-body-balance-board system, combined with the Lagrange 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 of the balance board pivot is established, the torsional stiffness and time delay of which are adjustable, for simulating uneven ground or external environment;

[0010] Step 3, based on the human-body-balance-board dynamics model, a passive rotation moment model of the ankle, knee and hip joints is established, the passive torque size of which is determined by the inherent passive damping and stiffness at the joint;

[0011] Step 4, based on the human-body-balance-board dynamics model, an active control moment model of the ankle, knee and hip joints is established, the active control torque size of which is determined by the proprioception, vestibular and visual feedback gain and reaction time delay factor;

[0012] Step 5, combined with the human-body-balance-board dynamics model and all joint control moment models, a human-body-balance-board control system model is formed;

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

[0014] Compared with the prior art, the present application has the following 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, while the present application can more accurately simulate the complex dynamic behavior of the human body in the sagittal plane balance through the dynamic interaction of multiple joints at the same time.

[0016] (2) Introducing adjustable stiffness and time delay balance board: in the present application, the dynamic interaction of the balance board is included in the model, so that the simulation can more realistically simulate the dynamic changes in the external environment influence and balance ability detection training.

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

[0018] (4) The model is more comprehensive and realistic: the numerical simulation method provided by the application comprehensively considers the biomechanical interaction of joints, the physical characteristics of the balance board, the neural feedback and its time delay, can more comprehensively and accurately simulate the dynamic process of human body balance, and thus provides strong theoretical support and guidance for in-depth study of human body balance mechanism and optimization of exercise training and rehabilitation scheme. BRIEF DESCRIPTION OF DRAWINGS

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

[0020] Figure 2 A flowchart of the numerical simulation method provided by the application.

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

[0022] Wherein, (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 A motion result diagram of the human body-balance board model under the second set of parameter conditions provided by the embodiment of the application:

[0024] Wherein, (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. DETAILED DESCRIPTION

[0025] In order to make the purpose, technical scheme and advantages of the embodiments of the application more clear, the technical scheme in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application.

[0026] The values of the physical parameters of the model in this embodiment are selected for demonstration of simulation calculation, and the parameter values can be selected by the user according to the specific situation or different human bodies in practice when the model is used. Obviously, the described embodiments are part of the embodiments of the application, rather than all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the application.

[0027] The following will be described in detail with reference to the accompanying drawings. Figures 1-4 The embodiments of the application will be further described in detail.

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

[0029] Step 1, based on the human-body- balance-plate system, combined with the Lagrange principle, the human-body- balance-plate dynamics model is established.

[0030] S1.1, the model is a sagittal plane model of a human body standing on a balance plate. The model is specifically a sagittal plane model of a human body standing on a balance plate, wherein the feet are coupled with the balance plate, and the rest is composed of three parts of lower leg, upper leg, and upper body, which are connected by ankle, knee, and hip joints; the balance plate is connected with the ground by a revolute pair, and the connection has adjustable passive rotational stiffness, and the balance plate provides a way to simulate uneven ground or unstable external environment; the control moments at each joint of the model consider the neural feedback that affects human balance, such as proprioception, vestibular sensation, and visual feedback, as well as the neural reaction time delay.

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

[0032] The physical parameters of the human body model are selected, such as the mass, length, and moment of inertia of each part of the body. Referring to GB / T17245-2004 "National Standard for Inertial Parameters of Chinese Adult Human Body" and GB / T 10000-2023 "Chinese Adult Human Body Size", the physical parameters of a 70kg, 180cm tall human body are selected, and 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 1 Physical parameters of 70kg and 180cm human body

[0034]

[0035]

[0036] S1.2, the human-body- balance-plate model is modeled with the pivot of the balance plate as the origin of the absolute coordinate system, and the rotation angles of the balance plate, ankle joint, knee joint, and hip joint are represented as q0, q1, q2, and q3, respectively, as shown in Figure 1 . Then the centroid position coordinates of the balance plate and the feet, lower leg, upper leg, and upper body (x0, y0, x1, y1, x2, y2, and x3, y3) are represented as:

[0037]

[0038] The Lagrange function value L of the human-body- balance-plate system is represented as:

[0039] L = T - V,

[0040]

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

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

[0043]

[0044] The decomposable expression is:

[0045]

[0046] where q k is the independent generalized coordinate of the particle system, is the first derivative of q k , Q k is the generalized force corresponding to q k , and t is time.

[0047] Thus, the dynamic model of the human-body- balance-plate system is:

[0048]

[0049] where q(t), and represent the angular displacement, angular velocity, and angular acceleration vectors 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 plate pivot, ankle joint, knee joint, and hip joint, respectively. D(·) is the inertia matrix, C(·) is the Coriolis term, and G(·) is the gravity term, whose expressions are:

[0051]

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

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

[0054]

[0055] D 12 = D 21 = I1+I2+I3+L1 2 m2+L1 2 m3+L22 m3 + m1 r1 2 + m2 r2 2 + m3 r3 2 + L0 m3 r3 cos(q1 + q2 + q3)

[0056] + L0 (L2 m3 + m2 r2) cos(q1 + q2) + 2L1 m3 r3 cos(q2 + q3) + L0 (L1 m2 + L1 m3 + m1 r1) cos(q1)

[0057] + 2L1 (L2 m3 + m2 r2) cos(q2) + 2L2 m3 r3 cos(q3),

[0058] D 13 = D 31 = I2 + I3 + L2 2 m3 + m2 r2 2 + m3 r3 2 + L0 (L2 m3 + m2 r2) cos(q1 + q2) + L1 m3 r3 cos(q2 + q3)

[0059] + L1 (L2 m3 + m2 r2) cos(q2) + 2L2 m3 r3 cos(q3) + L0 m3 r3 cos(q1 + q2 + q3),

[0060] D 14 = D 41 = I3 + m3 r3 2 + L1 m3 r3 cos(q2 + q3) + L2 m3 r3 cos(q3) + L0 m3 r3 cos(q1 + q2 + q3),

[0061]

[0062] D 24 = D 42 = I3 + m3 r3 2 + L1 m3 r3 cos(q2 + q3) + L2 m3 r3 cos(q3), D 33 = I2 + I3 + m2 r2 2 + m3 r3 2 + m3 L2 2 + 2m3 L2 r3 cos(q3),

[0063] D 34 = D 43 = I3 + m3 r3 2 + L2 m3 r3 cos(q3),

[0064] D 44 = I3 + m3 r32 .

[0065] Coriolis force matrix The specific expression is:

[0066]

[0067] The specific expression of the gravity term matrix G(q) is:

[0068]

[0069] G3 = -g(m3L2 + m2r2)sin(q0 + q1 + q2) - gm3r3sin(q0 + q1 + q2 + q3),

[0070] G4 = -gm3r3sin(q0 + q1 + q2 + q3).

[0071] Step 2, based on the human-body- balance-board dynamics model, a torsional moment model at the pivot of the balance board is established, with adjustable torsional stiffness and time delay, to simulate uneven ground or external environment.

[0072] S2.1, in the human-body-balance-board model, the balance board is coupled with 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.

[0073] S2.2, the hinge where the balance board connects with the ground has a torsional spring with adjustable stiffness, and the torsional moment also includes a time delay to simulate the effect of uneven ground or unstable environment on human balance. The torsional moment model at the pivot of the balance board is:

[0074] M b = K b q0(t-τ b )

[0075] Where M b represents the torsional moment of the torsional spring on the balance board, K b is the torsional spring stiffness, q0 is the balance board angle, and τ b is the time delay of the balance board feedback moment.

[0076] Step 3, based on the human-body-balance-board dynamics model, a passive rotation moment model at the ankle, knee and hip joints is established, and the size of the passive moment is determined by the inherent passive damping and stiffness at the joints.

[0077] S3.1 The moment generated at the ankle, knee and hip joints in the human-body-balance-board model is composed of active and passive moments, which can be represented as:

[0078] M1 = M 1,passive + M 1,active

[0079] M2 = M 2,passive + M 2,active

[0080] M3 = M 3,passive + M 3,active

[0081] where M i,active is the active torque at each joint, M i,passive is the passive torque at each joint, i = 1, 2, 3.

[0082] S3.2 The passive torque is originated from the inherent muscle stiffness and damping, and acts rapidly in response to the change of joint angle, so the passive torque model at ankle, knee and hip joints is a instantaneous nonlinear proportional derivative controller, which is expressed as:

[0083]

[0084] where K ma , K mk and K mh are the passive muscle stiffness at ankle, knee and hip joints, respectively. C ma , C mk and C mh are the passive muscle viscous damping coefficients at ankle, knee and hip joints, respectively. β is a dimensionless parameter, which represents the nonlinear relationship between the force and the stretch of the muscle involved in the postural control.

[0085] Step 4, based on the human-body- balance-board dynamics model, the active control torque model at ankle, knee and hip joints is established, the size of which is determined by the proprioceptive, vestibular and visual feedback gains and the reaction time delay factor.

[0086] S4.1 In the process of controlling balance, the neuromuscular system needs time to receive and process sensory signals, and muscle contraction also needs time, so the effect of time delay on active control torque should be considered here.

[0087] S4.2 The active control torque at ankle, knee and hip joints in the human-body- balance-board model also needs to consider the neural feedback gain that affects human balance, including proprioceptive, vestibular and visual feedback gain. Among them, the proprioceptive system perceives the relative position information between different parts of the body, so it provides joint angle information in the local reference frame, while the vestibular and visual systems can perceive the position relationship between the body and the external environment, so it provides angle information of each part of the body in the absolute reference frame.

[0088] S4.3 According to the influencing factors of active torque, the active control torque model at ankle, knee and hip joints is a time-delay proportional controller, which is expressed as:

[0089] M 1,active = K pa q1(t-τ1) + K va (q0(t-τ1) + q1(t-τ1))

[0090] M 2,active = K pk q2(t-τ2) + K vk (q0(t-τ2) + q1(t-τ2) + q2(t-τ2))

[0091] M 3,active = K ph q3(t-τ3) + K vh (q0(t-τ3) + q1(t-τ3) + q2(t-τ3) + q3(t-τ3))

[0092] where K pa , K pk and K ph represent the proprioceptive gains at the ankle, knee and hip joints respectively. K va , K vk and K vh represent the visual-vestibular combined feedback gains at the ankle, knee and hip joints respectively. The reaction time delays for the torque generation at the ankle, knee and hip joints are represented by τ1, τ2 and τ3 respectively.

[0093] Step 5, combine the human-body- balance-board dynamics model with all the joint control torque models to form the human-body- balance-board control system model.

[0094] Combine the human-body- balance-board dynamics model with all the joint control torque models to form the human-body- balance-board control system model. Substitute the ankle, knee and hip joint torque models and the balance-board torque model into the human-body- balance-board dynamics model, then the human-body- balance-board control system model is:

[0095]

[0096] Step 6, input the human-body- balance-board control system model into a mathematical modeling software, and use the software to perform numerical simulation analysis on the model.

[0097] There is an unknown parameter vector η = [K b , K pa , K pk , K ph , K va , K vk , K vh , K ma , K mk , K mh , C ma , Cmk ,C mh ] and time delay τ = [τ b ,τ1,τ2,τ3]. To consider the correlation between control parameters and reduce the number of parameters to simplify the model, some assumptions in human balance biomechanics are needed.

[0098] 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 is 20% and 10% larger than that of the ankle joint, respectively, i.e. ph = 1.2K pa = 1.2K vh = 1.2K va = 1.1K pk = 1.1K pa = 1.1K vk = 1.1K va .

[0099] Second, for the purpose of normalization, K cr = mgh is defined, which represents the critical ankle joint stiffness required for the human body to stand on a rigid ground and maintain stability when the human body is regarded as a rigid single-degree-of-freedom ankle joint model, where m is the total mass of the lower leg, upper leg, and upper body, g is the gravitational acceleration, and h is the distance from the center of mass of the lower leg, upper leg, and upper body to the ankle joint. The ratio and represent the relative stiffness of the muscle stiffness of the active control torque, i.e. and are dimensionless. Therefore, after simplification, the variables K pa , K pk , K ph , K va , K vk , K vh in the system affecting the active control torque are determined only by and . Similarly, the relative stiffness of the balance board torsion torque is defined as

[0100] For K ma , K mk , K mh , C ma , C mk , C mh These control muscles are passive torque parameters that are not variable, and their parameter values are set to K ma = 0.6K cr , 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 .

[0101] For the parameters in the model that need to be studied and time delay τ = [τ b , τ1, τ2, τ3], the specific parameter values can be set according to the research objectives.

[0102] In the MATLAB environment, the control system model of the human-body balance board is numerically simulated, and the motion law and stability of each part of the body under different neural sensory feedback gains and time delays are observed. The conditions are set as follows: the initial angular displacement and angular velocity of the system in all cases are respectively set as q(0) = [-0.1-0.1-0.1-0.1] T rad and

[0103] The following two groups of parameters are arbitrarily selected for numerical simulation of the model, and the motion results are shown in Figures 3-4 .

[0104] 1. Select τ = [τ b , τ1, τ2, τ3] = [1, 10, 10, 10] ms, and the results are shown in Figure 3 .

[0105] 2. Select τ = [τ b , τ1, τ2, τ3] = [1, 50, 50, 50] ms, and the results are shown in Figure 4 .

Claims

1. A numerical simulation method of a human-body-slab control system model, characterized by, The method comprises: Step 1, based on the human-body-tiltboard system, a human-body-tiltboard dynamics model is established by combining the Lagrange principle: where the elements of the rotation matrix q(t) = [q0 q1 q2 q3] T correspond to the rotation angles of the plate, ankle, knee and hip, respectively; while and denote the angular velocity and angular acceleration vectors of the respective joints; the elements of the moment matrix M = [M b M1M2 M3] T correspond to the moments at the plate-ground hinge, ankle, knee and hip, respectively; D(·) is the inertia matrix, C(·) is the Coriolis term, and G(·) is the gravitational term. Step 2, based on the human-body-tiltboard dynamics model, a torsional moment model of the tiltboard pivot is established, the torsional stiffness and time delay of which are adjustable, and is used to simulate the uneven ground or external environment; Step 3, based on the human-body-tiltboard dynamics model, passive rotation moment models of the ankle, knee and hip joints are established, the passive torque of which is determined by the inherent passive damping and stiffness of the joints; Step 4, based on the human-body-tiltboard dynamics model, active control moment models of the ankle, knee and hip joints are established, the active control torque of which is determined by the proprioception, vestibular feedback gain and reaction time delay factors; Step 5, by combining the human-body-tiltboard dynamics model and all the joint control moment models, a human-body-tiltboard control system model is formed; Step 6, the model of the human-body-tiltboard control system is input into a mathematical modeling software, and numerical simulation analysis is performed on the model by using the software.

2. The numerical simulation method of a human-body balance board control system model according to claim 1, wherein, In step 1, the dynamics model of the human-body-tiltboard system is established as follows: S1.1, the human-body-tiltboard dynamics model is a sagittal plane model of the human body standing on the tiltboard; the basic structure of the model comprises a tiltboard, a lower leg, an upper leg and an upper body, and each part is regarded as a rigid body; S1.2, the Lagrange function value L of the human-body-tiltboard system is represented as: L = T - V, wherein T is the kinetic energy of the system, and V is the potential energy of the system; S1.3, according to the Euler-Lagrange dynamics equation: where q k is the independent generalized coordinate of the system of particles, is the first derivative of q k , Q k is the generalized force corresponding to q k , and t is time. Thus, the dynamics model of the human-body-tiltboard system is obtained as: where the elements of the rotation matrix q(t) = [q0 q1 q2 q3] T correspond to the rotation angles of the plate, ankle, knee and hip, respectively; while and denote the angular velocity and angular acceleration vectors of the joints, respectively; the elements of the moment matrix M = [M b M1M2 M3] T correspond to the moments at the plate-ground hinge, ankle, knee and hip, respectively; D(·) is the inertia matrix, C(·) is the Coriolis term, and G(·) is the gravitational term.

3. The numerical simulation method of human balance board control system model according to claim 1, wherein, Step 2 comprises the following steps: S2.1, in the human-body-tiltboard model, the coupling of the tiltboard and the foot has a concentrated mass; the line connecting the ankle joint and the tiltboard ground hinge should be perpendicular to the plane of the tiltboard; S2.2, the pivot of the tiltboard and the ground has a torsional spring with adjustable stiffness and time delay, to simulate the effect of the uneven ground or unstable environment on the human body balance; the torsional moment model of the tiltboard pivot is: M b = K b q0(t-τ b ) where M b represents the torque of the torsion spring to 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 balance plate.

4. The numerical simulation method of a human-body balance board control system model according to claim 1, wherein, Step 3 comprises the following steps: S3.1, for the torque generated at the ankle, knee and hip joints in the human-body-tiltboard model, the torque is composed of active torque and passive torque, and is represented as: M1 = M 1,passive +M 1,active M2 = M 2,passive + M 2,active , M3 = M 3,passive +M 3,active where M i,active is the active torque, M i,passive is the passive torque, i = 1,2,3; S3.2, the passive torque is derived from the inherent muscle stiffness and damping, and rapidly acts as a response to the change of the joint angle, so the passive torque model at the ankle, knee and hip joints is an instantaneous nonlinear proportional derivative controller, and is represented as: In the formula K ma K mk and K mh These represent the passive muscle stiffness at the ankle, knee, and hip joints, respectively; C ma C mk and C mh These represent the passive viscous damping coefficients of the muscles at the ankle, knee, and hip joints, respectively. β is a dimensionless parameter, representing the nonlinear relationship between the force and the stretching amount of the muscle participating in the posture control.

5. The method of claim 1, wherein the human balance board control system model is simulated numerically. Step 4 comprises the following steps: S4.1, in the process of controlling the balance, the neuromuscular system of the human body needs time to receive and process the sensory signals, and the muscle contraction also needs time, so the joint active control torque in the human-body-tiltboard dynamics model should consider the influence of time delay; S4.2、The active control torque of ankle, knee and hip joint in human-body-tilt-board model also needs to consider the neural feedback gain which affects human body balance, including proprioceptive, vestibular and visual feedback gain; wherein, the proprioceptive system senses the relative position information between each part of the body, so it provides the joint angle information in the local reference frame, while the vestibular and visual system can sense the position relationship between the body and the external environment, so it provides the angle information of each part of the body in the absolute reference frame; S4.3、According to the influencing factors of active torque, the active control torque model of ankle, knee and hip joint is a time-delay proportional controller, 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 represent the somatosensory feedback gains at the ankle, knee and hip joints, respectively; K va , K vk and K vh represent the visual-vestibular combined feedback gains at the ankle, knee and hip joints, respectively; and τ1, τ2 and τ3 represent the reaction time delays for torque generation at the ankle, knee and hip joints, respectively.

6. The method of claim 1, wherein the human balance board control system model is simulated numerically. Step 5 comprises the following steps: The human body - balance board control system model is formed by combining the human body - balance board dynamics model and the joint torque model. The ankle, knee and hip joint torque and the balance board torque model are substituted into the human body - balance board dynamics model, and the human body - balance board control system model is: .

7. The method of claim 1, wherein the human balance board control system model is simulated numerically. Step 6 comprises the following steps: The human-body-tilt-board control system model is input into the mathematical modeling software; according to the research target and research object, all physical parameter values of the model can be determined by itself, and then the software is used to carry out numerical simulation analysis on the control system model.

Images