RU2277373C2 - Method for estimating forces and moments using feedback - Google Patents

Abstract

FIELD: medicine.

SUBSTANCE: method involves determining articulation loading under direct dynamics modeling. Direct dynamics unit determines modeled kinematic data. Error correction controller reduces following error to zero between the modeled kinematic data and measured kinematic data. It produces modified acceleration to be introduced into reverse dynamics unit. Special-purpose device and machine-readable carrier are available for determining articulation load estimation.

EFFECT: high accuracy of data received.

36 cl, 24 dwg

Description

Link to related applications

This application is related to provisional application for US patent No. 60/301891, filed June 29, 2001, for the invention of "Recursive nonlinear method using feedback to evaluate the forces and moments of joints based on kinesiology measurements" and provisional application for US patent No. 60/353378, filed January 31, 2002, for the invention, “Direct Solutions to Inverse Dynamics Problems: Feedback Linearization Method,” based on which priority is claimed under USC 35 par. 119 (a).

A. The technical field to which the invention relates

The present invention relates to the analysis of human movements, in particular to the analysis of the forces and moments of joints using nonlinear feedback in direct modeling of dynamics.

B. Description of the Related Art

When studying human movements, an analysis of the inverse (inverse) dynamics is usually used to assess the strength and moments of the joints. In a conventional analysis of the inverse dynamics, the strengths and moments of the joints are calculated from observations of segmental movement. An analysis of the inverse dynamics is usually used to solve problems of biomechanics, since the internal strength of human joints cannot be measured in a simple way. However, it is possible to measure the segmental movements and derive the angles of the joints from the measured displacement to determine the forces and moments of the respective joints.

One of the problems of using reverse dynamics in the study of human movements is the occurrence of an error caused by the calculation of higher order derivatives to determine the forces and moments of joints. Methods using the concept of inverse dynamics in biomechanics work well if the input signals are noise-free and the dynamic model is flawless. However, experimental observations are imperfect and contain noise. Sources of noise are both the measuring device and the joint itself. Inverse dynamics methods for calculating joint moments require the calculation of higher order derivatives based on experimental observations. In particular, the angular acceleration term is the second derivative of the joint angle, and linear acceleration is the second derivative of the center of mass acceleration. Numerical differentiation of experimental observations increases noise. Of particular importance for solving the problem of calculating speeds and accelerations is the presence of high-frequency noise. The amplitude of each of the harmonics increases with an increase in its harmonic number: velocities increase linearly, and accelerations increase in proportion to the square of the harmonic number. For example, the second-order differentiation of a signal with high-frequency noise ω can result in a signal with frequency components ω ² . As a result of such a parabolic amplification of noise, erroneous calculations of the forces and moments of the joints are obtained.

Although noise filtering methods exist, such filtering is difficult to implement and time consuming, since it requires a lot of analysis to separate the true signal in biomechanical data from noise. For example, low-pass filtering is commonly used to reduce high-frequency errors. However, the difficulty of low-pass filtering is to select the optimal cutoff frequency f _c . Since there is no general solution for choosing optimal filtering parameters, the results of filtering methods are often unreliable.

To assess the strengths and moments of the joints without errors due to the usual analysis of the inverse dynamics, approaches based on optimization were proposed. Unlike inverse dynamics, optimization-based methods do not require numerical differentiation. However, the use of optimization-based solutions is limited, because these methods require large computational costs, do not guarantee convergence, and are usually very difficult to implement.

Another problem associated with the use of inverse dynamics for the analysis of human movements is that the inverse method does not allow predicting the nature of new movements. With the inverse dynamics, the forces and moments are calculated from the observed reactions. Prediction of new movements requires calculating the reaction expected as a result of the application of forces and moments. An analysis of the inverse dynamics does not allow forecasting, since the forces and moments are calculated, and not the reaction expected as a result of the application of these forces and moments.

Thus, there is a need for a computationally efficient system and method that: (1) is able to evaluate joint forces and moments without errors due to higher order derivatives; (2) do not require a closed analysis of the whole body in a closed form; and (3) allow predicting the nature of human movements.

Summary of the invention

One embodiment of the present invention makes it possible to evaluate loads on human joints. The load on the joint includes the forces and moments acting on the joint. The direct dynamics module determines kinematic data by numerically integrating (or modeling) the dynamic equations of motion. The error correction controller nullifies the tracking error between the kinematic data obtained from direct modeling and the measured (or desired) kinematic data. The error correction controller generates a modified acceleration for input into the inverse dynamics module. In one embodiment, the modified acceleration is a value determined without taking into account the second derivative of the measured (or desired) kinematic data. Thus, the estimated joint load when it is entered into the direct dynamics module monitors the measured (or desired) kinematic data without errors associated with the calculation of higher derivatives of “noisy” kinematic data.

In another embodiment, joint loads are evaluated recursively for a planar, sequentially coupled system. With the recursive method, the process begins at the first end of the sequential chain of segments, and joint loads are calculated toward the second end of the sequential chain. The segments in this chain are interconnected by joints, and the forces and moments of reactions in the joint are common to two interconnected segments. Joint loads estimated for the first segment are used in the evaluation for the next segment until the joint or joints of interest are reached. This means that the result of the recursion is the calculation of forces and moments at the junction point for the next segment. This result is used as input (input) for the analysis of the next segment. Therefore, the recursive method does not require modeling the dynamics of the whole body. Although in a particular case a recursive modeling of the dynamics of the whole body may be required, nevertheless, the recursive method provides flexibility that can reduce the sources of error.

Recursive options include estimates of an open (open) circuit and estimates of a closed (closed) circuit. An open-circuit system is limited to the environment at one end, and the remaining terminal segments are free. In a closed-circuit system, more than one end is in contact with the medium. The communication system segments are numbered in recursion order, from segment 1 to segment n, which is the last segment to be considered. Segment n does not have to be the last segment in a system of multiple bodies. Rather, the segment n is taken to be the segment on which it is desirable to stop the recursive calculation, since all the forces and moments of interest have already been found. To initiate a recursion, you must have the force and moment acting on the first segment. For example, when analyzing human movements, the reaction forces of the base (support reaction) under the legs, which initialize the recursive equations, are usually measured. The use of support reaction forces increases the accuracy of estimates of the load on joints located in close proximity to the base.

In another embodiment, the tracking system according to the invention can be applied to closed-shape speakers. The equations of a closed-form system for a system of an unbounded rigid body are described by the number n of differential equations. Like the described options using recursion, the control law is used here to linearize and separate (decouple) the dynamics of the system.

Other features of the invention, its essence and various advantages will be more apparent from the accompanying drawings and detailed description.

Brief Description of the Drawings

The accompanying drawings, which are part of the materials of this application, illustrate several embodiments of the invention and, together with the description, serve to explain the principles of the present invention.

Figure 1 illustrates how recursive computation can be used to separate the dynamics of the lower body from the dynamics of the upper body,

figure 2 depicts a diagram of the forces of a free body acting on segments in a planar series-connected system with an open circuit,

figure 3 depicts a diagram of a free body for one segment in a series-connected system,

4 is a structural diagram of a tracking system for communication segment i,

5 is a structural diagram of a tracking system for communication segment i, illustrating in more detail the error correction controller,

6 is a flowchart illustrating a recursive tracking process,

7 is a free body diagram illustrating a two-dimensional system of three segments,

figa-8C depict graphs illustrating the tracking accuracy for displacement of the ankle joint of Fig.7 using small feedback coefficients and excluding accelerations,

figa-9C depict graphs illustrating the tracking accuracy for the displacement of the knee joint of Fig.7 using small feedback coefficients and excluding accelerations,

figa-10C depict graphs illustrating the tracking accuracy for the forces and moments of the knee joint of Fig.7 using small feedback coefficients and excluding accelerations,

11A-11C are graphs illustrating tracking accuracy for the forces and moments of the hip joint of FIG. 7 using small feedback coefficients and excluding accelerations,

figa-12C depict graphs illustrating the tracking accuracy for displacement of the ankle joint of Fig.7 using small feedback coefficients and taking into account accelerations,

figa-13C depict graphs illustrating the tracking accuracy for displacement of the knee joint of Fig.7 using small feedback coefficients and taking into account accelerations,

figa-14C depict graphs illustrating the tracking accuracy for the forces and moments of the knee joint of Fig.7 using small feedback coefficients and taking into account accelerations,

figa-15C depict graphs illustrating the tracking accuracy for the forces and moments of the hip joint of Fig.7 using small feedback coefficients and taking into account accelerations,

figa-16C depict graphs illustrating the tracking accuracy for displacement of the ankle joint of Fig.7 using large feedback coefficients and excluding accelerations,

figa-17C depict graphs illustrating the tracking accuracy for displacement of the knee joint of Fig.7 using large feedback coefficients and excluding accelerations,

figa-18C depict graphs illustrating the tracking accuracy for the forces and moments of the knee joint in Fig.7 using large feedback coefficients and excluding accelerations,

figa-19C depict graphs illustrating the tracking accuracy for the forces and moments of the hip joint of Fig.7 using large feedback coefficients and excluding accelerations,

figa-20C depict graphs illustrating tracking accuracy for displacement of the ankle joint of Fig.7 using large feedback coefficients and taking into account accelerations,

figa-21C depict graphs illustrating the tracking accuracy for displacement of the knee joint of Fig.7 using large feedback coefficients and taking into account accelerations,

figa-22C depict graphs illustrating the tracking accuracy for the forces and moments of the knee joint of Fig.7 using large feedback coefficients and taking into account accelerations,

figa-23C depict graphs illustrating the tracking accuracy for the forces and moments of the hip joint of Fig.7 using large feedback coefficients and taking into account accelerations,

Fig.24 is a graph illustrating the error for displacement of the ankle joint in Fig.7.

Description of preferred embodiments of the invention

Preferred embodiments of the present invention are described below with reference to the accompanying drawings, in which identical or functionally similar elements are denoted by the same reference numbers. In addition, the left digit of each reference number in the figures corresponds to the figure in which this number was used for the first time.

Figure 1 presents an illustration depicting how recursive calculations are used to separate the dynamics of the lower body from the dynamics of the upper body. The illustration shows the upper part 105 of the body and the lower part 110 of the body. One segment of the upper body part 105 is shown with a load of 140. The lower body part 110 contains segments having an ankle joint 120, a knee joint 125 and a hip joint 130. With the recursive method for calculating joint forces and moments, the upper body part 105 can be modeled separately from the lower part 110 bodies. Starting from the base opposing forces 115 (support reactions), it is possible to effectively isolate the joints 120, 125 and 130 of the lower part 110 of the body, as well as the parameters of the communication segments associated with them from the upper part 105 of the body. This means that the internal forces and moments acting on the joints 120, 125 and 130 can be estimated without taking into account the effects caused by the load 140 and the physical parameters of the upper body 106, such as mass, center of mass, inertia and segment length. These parametric uncertainties of the upper part of the body 105 are important sources of errors in evaluating the internal forces and moments in the human body when the closed-body dynamics procedures are used. In contrast to the closed-loop solution for the whole body, the variants of the recursive solution use measurements of the forces 115 of the reaction of the support as limitations for the recursive calculation of the moments of the joints, starting from the base (support) and moving upwards, for example, to the knee joint 125 and the hip joint 130 .

Using the recursive method to assess the strengths and moments of joints allows you to focus on the joints of interest without introducing additional sources of error. In addition, a recursive method with measurement of the support reaction forces 115 as input provides, for example, an additional measurement modality. That is, combining information about kinematics and reaction force provides an additional opportunity to increase the reliability of the obtained estimates of internal forces. A person may be exposed to unpredictable loads or dynamics constraints as a result of interaction with other objects or other people in the environment. Such circumstances can alter the dynamic presentation needed to evaluate the internal forces and moments in the joints. Some applications for using the recursive method in these circumstances include biomechanical studies of lifting tasks and the development of control for assistive devices that help people with physical disabilities perform their daily tasks. Specialists understand that to provide additional modalities of perception, intended for use in assessing various forces and moments, force and pressure sensors built into shoes can serve.

A. Recursive method for a two-dimensional system with a serial circuit

Embodiments of the present invention are applicable to planar systems including a recursive open circuit and a recursive closed circuit. In an open-circuit system, at most one end of the system, consisting of many bodies, is in contact with the environment. The other end or ends are free or not limited. In a closed-circuit system, more than one end is in contact with the environment.

Figure 2 shows a diagram of the forces of a free body acting on segments in a planar series-connected system with an open circuit. The system includes a first segment 205, a second segment 210 and an nth segment 215. Segments 205, 210 and 215 are connected by articulated joints (pivot joints). Each of the segments 205, 210, and 215 is illustrated as a free body diagram in which the segments are connected by a first joint 220 (hinge), a second joint 222 (hinge), a third joint 224 (hinge), and an nth joint 226 (hinge). The first segment 205 includes a first joint 220 and a second joint 222. The second segment 210 includes a second joint 222 and a third joint 224. In particular, segments 205 and 210 are connected as follows: second joint 222 connects the first segment 205 to the second segment 210 Thus, a serial chain of n segments is formed by connecting n segments with a common or overlapping joint.

For each of the joints 220, 222, 224 and 226, the moments of rotation of the joints, the horizontal reaction forces and the vertical reaction forces of each joint, which are designated as τ _I , F _i and G _i , respectively, are shown. For example, for the first joint 220, the rotation moment τ _I , the horizontal reaction force F _i and the vertical reaction force G _{i are} illustrated. An example of a recursive calculation is described below with reference to FIG. In recursive computation, a system of multiple bodies is conceptually divided into separate segments. The free body diagram of each segment is analyzed. The segments are interconnected by joints (hinges), for example, the second joint 222. Reaction forces and moments, for example on the second joint 222, are common for the first segment 205 and the second segment 210. The analysis begins with the first segment 205, and the force and moment in the attachment point of the second segment 210, i.e. on the second joint 222 (hinge). The calculated forces and moment at the second joint 222 are the result of recursion 1. This result is used as input to analyze the next segment, for example, the second segment 210. The recursive analysis of the segments continues until the nth segment 215 is reached. This n segment 215 is the segment of interest or segment on which it is desired to stop recursive computation. In an embodiment where the support reaction forces 115 act on the first segment 205 (FIG. 1), the forces and moment acting on the second joint 222 are calculated based on the forces and moment acting on the first joint 220. Then, the forces and moment acting on the third joint 224, based on previously calculated forces and the moment acting on the second joint 222. This recursive procedure of using the result of dynamic calculations as input for the next calculation is repeated until the forces and moments for representing inter eu joint or joints. One skilled in the art will recognize that the nth segment 215 is not necessarily the last segment in a plurality of bodies. Rather, the nth segment refers to the segment on which it is desirable to stop the recursive calculation, because the forces and moments of interest will already be found. It should also be noted that the support reaction forces 115 act at the contact point, which is not necessarily located on the joint. Additional details of these calculations will be described below with reference to FIG.

), угол сустава относительно вертикали - θ_i и угловое ускорение -

. Как показано на фиг.3, физические параметры для сегмента i тела включают в себя: массу m_i, момент инерции I_i, длину L_i сегмента и длину k_i до центра масс. Также на фиг.3 для каждого сустава 310 и 315 показаны моменты вращения τ_i суставов, горизонтальные силы F_i реакции и вертикальные силы G_i реакции. Далее представлены уравнения Ньютона-Эйлера для вычисления сил и моментов на каждом из суставов 310 и 315 сегмента i тела в уравнениях 1, 2 и 3.Figure 3 shows a diagram of a free body for one segment in a series-connected system. Segment 305 is the i-th segment of a planar series-connected system, for example, the system illustrated in FIG. 2. Body segment i includes joint i (310) and joint i + 1 (315). For an isolated segment i, where i = 1 ... n, the acceleration of the center of mass is denoted as (

), the angle of the joint relative to the vertical is θ _i and the angular acceleration is

. As shown in FIG. 3, the physical parameters for the body segment i include: mass m _i , moment of inertia I _i , segment length L _i and length k _i to the center of mass. Also, FIG. 3 shows for each joint 310 and 315 the moments of rotation τ _{i of the} joints, the horizontal reaction forces F _i and the vertical reaction forces G _i . The following are the Newton-Euler equations for calculating the forces and moments on each of the joints 310 and 315 of the body segment i in equations 1, 2 and 3.

Those skilled in the art will understand that Equation 1 is an expression for the addition of forces acting on a body segment 305 in projection onto the x axis, or horizontal direction. Similarly, equation 2 is an expression for the addition of forces acting on a segment of the body 305 in projection onto the y axis, or the vertical direction. In equation (2), g denotes the acceleration of gravity. Equation 3 is an expression for the addition of angular accelerations acting on joints 310 and 315.

1. The technique of inverse dynamics

When analyzing the inverse dynamics, the forces and moments acting on the joints are calculated from the measured or desired kinematic data. Kinematic data include the coordinates of the center of mass and joint angle data. In one embodiment of the present invention, a recursive solution for calculating the forces and moments on each joint can be obtained from the compact representation (in the form of a matrix) of the Newton-Euler equations in the form of equation 4 shown below. In equation (4), U _i = [F _i G _i τ _I ] ^T is a vector (transposed) whose elements correspond to horizontal force, vertical force and moment, respectively, acting on joint i (310). The forces and moment on the joint i + 1 (315) are described as U _{i + 1} . Other details of the recursive solution for U _i and U _{i + 1} will be described below.

в уравнении 4 представляет вторую производную вектора q_i. Элементы уравнения 4 более подробно определены следующим образом:The vector q _i = [x _i y θ _I ] ^T represents the coordinates of the center of mass and the angle of the joint for joint i. Professionals understand that a member

in equation 4 represents the second derivative of the vector q _i . The elements of equation 4 are defined in more detail as follows:

2. Open Circuit Rating

As described above, an open-circuit system has one end in contact with the environment. The end in contact with the environment is called the “limited end”. In one embodiment of the present invention, the limited end is the legs of a person in contact with a base or other supporting surface. In one embodiment, the kinematic data is supplemented by measurements of the support reaction forces 115 (denoted as U ₁ ) to increase the accuracy of the estimates of inertia and moment. The segments are numbered upward from the base, from 1 to n, where n is the last segment to be considered. Thus, the Newton-Euler reverse dynamics technique uses measurements of forces and moments underfoot. For U ₁ , used as the boundary condition on segment 1, the force and moment on segment i, where i has a value from 1 to n (i: 1 → n), are calculated sequentially using equation 5, starting from segment 1 and moving to segment n. In an open-chain evaluation, where n is the last segment in the chain, there are no external forces acting on n, so that U _{n + 1} = 0.

Since noise and measurement errors occur in the biomechanical model, the boundary condition on the free segment is usually violated. In other words, in the variant with an (open) chain, where recursion goes from segment 1 to a free segment (denoted by n), U _{n + 1 is} not 0. This excessive determinism is resolved by adding residual forces and moments of rotation to segment n. The advantage of a recursive formulation with the numbering of segments from 1 to n is that there is no need to model the entire body. The evaluation of force and momentum ends on segment n, regardless of whether it is the last segment of a given sequential system or not. Parametric uncertainties for the upper limbs and uncertainties in the rigid body model are important sources of errors in evaluating internal forces and moments. However, these uncertainties of the upper limbs can be avoided when moments of only joints closest to the plane of force are required.

In another open-circuit version, only kinematic measurements are available. Segments are numbered from 1 to n, where segment 1 has a free end rather than a bounded end. Since segment 1 has a free end, U ₁ = 0 is the boundary condition for recursion towards segment n.

3. Closed circuit evaluation

In another embodiment of the present invention, a closed-loop assessment is performed. As described above, a closed-circuit system has more than one end in contact with the environment. In this embodiment, sensor measurements or other initial forces are needed to evaluate internal forces and moments. Segments are numbered sequentially, from segment 1 to segment n, which is the last segment of interest. The measurement data for the sensor or the initial force on segment 1 is designated as U ₁ , where U ₁ ≠ 0, because the end of segment 1 is limited. When measuring U ₁ , available as a boundary condition on segment 1, the force and moment on segment i, where i has a value from 1 to n (i: 1 → n), are calculated sequentially using equation 5, starting from segment 1 and moving forward to segment n.

B. Inverse solution using non-linear feedback

,

и

а также переменные q_i и

состояния. В одном варианте требуются измеренные или желательные кинематические данные (

) и оценки их скоростей (

). Оценки ускорения (

) можно использовать в применениях, не содержащих шума, однако они не являются необходимыми. Контроллер 405 коррекции ошибок выдает модифицированное ускорение

^° в качестве входных данных для модуля 410 обратной динамики. Модуль 410 обратной динамики имеет дополнительные входы U_i и q_i. Вектор U_i представляет силы и момент на суставе i. Выходные данные модуля 410 обратной динамики представляют оценки U_i+1 силы и момента для сустава i+1. Входные данные в модуль 415 прямой динамики 415 включают в себя U_i, U_i+1 и q_i. Кроме того, оцененные сила и момент U_i+1 сустава используется в качестве входных данных во время следующей итерации, где они обозначаются как U_i для приращенного i. В каждом случае итерации или рекурсии U_i является входными данными, а U_i+1 - результатом. Модуль 415 прямой динамики выдает переменные q_i и

состояния. Параметры для модуля прямой динамики (т.е. A_i, M_i, B_i и P_i) идентичны параметрам для обратной динамики.Figure 4 presents a structural diagram of a tracking system for segment i of the body. The error correction controller 405, the reverse dynamics module 410 and the forward dynamics module 415 are interconnected and form a tracking system. Input for error correction controller 405 includes kinematic data

,

and

as well as the variables q _i and

condition. In one embodiment, measured or desired kinematic data (

) and estimates of their speeds (

) Acceleration Estimates (

) can be used in noise-free applications, but they are not necessary. Error correction controller 405 provides modified acceleration

^° as input to the inverse dynamics module 410. The inverse dynamics module 410 has additional inputs U _i and q _i . The vector U _i represents the forces and moment on the joint i. The output of the inverse dynamics module 410 provides estimates of U _{i + 1} strength and moment for the joint i + 1. The input to the direct dynamics module 415 415 includes U _i , U _{i + 1} and q _i . In addition, the estimated joint strength and moment U _{i + 1} is used as input during the next iteration, where they are denoted as U _i for incremental i. In each case of iteration or recursion, U _i is the input, and U _{i + 1} is the result. The direct dynamics module 415 provides the variables q _i and

condition. The parameters for the forward dynamics module (i.e., A _i , M _i , B _i, and P _i ) are identical to the parameters for inverse dynamics.

^°. Модуль 415 прямой динамики вычисляет ускорения согласно уравнению 7 и затем осуществляет численное интегрирование ускорений для получения переменных q_i и

состояния, связанных с суставом i. Контроллер 405 коррекции ошибок использует обратную связь по переменным q_i и

состояния для формирования модифицированного ускорения

В одном варианте осуществления изобретения модифицированное ускорение

является значением, вычисленным без учета второй производной измеренных или желательных данных кинематики. Контроллер 405 коррекции ошибок формирует член модифицированного ускорения

таким образом, что модуль 410 обратной динамики вычисляет набор входных данных или управляющих данных, обозначенных как U_i+1, которые при вводе в модуль 415 прямой динамики последовательно воспроизводят или отслеживают измеренные или желательные данные

кинематики.In one embodiment of the invention, the strengths and moments of the joints are evaluated using the inverse dynamics module 410. Equation 6 represents the inverse dynamics control law for recursively calculating joint load data for U _{i + 1} using modified acceleration

^° . The direct dynamics module 415 calculates accelerations according to equation 7 and then numerically integrates the accelerations to obtain the variables q _i and

conditions associated with the joint i. The error correction controller 405 uses feedback on the variables q _i and

states for the formation of modified acceleration

In one embodiment, the modified acceleration

is the value calculated without taking into account the second derivative of the measured or desired kinematics data. Error correction controller 405 generates a modified acceleration term

so that the inverse dynamics module 410 calculates a set of input data or control data, designated as U _{i + 1} , which, when input to the direct dynamics module 415, sequentially reproduces or tracks the measured or desired data

kinematics.

состояния на основании вычисленных сил и момента. В частности, модуль 415 прямой динамики осуществляет численное интегрирование уравнения 7 для нахождения векторов положения и скорости, которые соответствуют поступившим данным U_i+1 нагрузки на сустав. В одном варианте численное интегрирование выполняют с помощью функции интегрирования, предусмотренной в программном продукте MATLAB компании MathWorks, Inc., Natick, Massachusetts. Специалистам понятно, что это интегрирование можно выполнять многими методами, например методами Рунге-Кутта. Переменные q_i и

состояния вводятся в контроллер 405 коррекции ошибки, который вычисляет модифицированное ускорение

^° для текущего шага времени. Начиная с исходных условий q_i (0) и продолжая до конечной точки, контроллер 405 коррекции ошибок сводит к нулю ошибку слежения между моделированными и измеренными (или желательными) кинематическими данными.The direct dynamics module 414 performs modeling to find the variables q _i and

states based on calculated forces and moment. In particular, the direct dynamics module 415 numerically integrates Equation 7 to find the position and velocity vectors that correspond to the received joint load data U _{i + 1} . In one embodiment, numerical integration is performed using the integration function provided in the MATLAB software product of MathWorks, Inc., Natick, Massachusetts. It will be understood by those skilled in the art that this integration can be accomplished by many methods, for example, Runge-Kutta methods. Q _i and

states are inputted to error correction controller 405, which calculates the modified acceleration

^° for the current time step. Starting from the initial conditions q _i (0) and continuing to the end point, the error correction controller 405 reduces to zero the tracking error between the simulated and measured (or desired) kinematic data.

Those skilled in the art will understand that the described equations, expressions, modules, or functions can be implemented in a universal computer, a specialized computer, or hardware. In one embodiment of the invention, the essential features of the invention are implemented by a universal computer, which is programmed with a special software product. This software product is preferably distributed on a computer-readable medium that includes software instructions. A computer-readable medium may be, for example, a read volume. Readable memory volumes can be obtained through a public computer network, personal computer network, or the Internet. It is understood that program instructions can be implemented in any appropriate form, for example, as source code, object code, or script code.

ошибки производной из кинематических данных, полученных в результате моделирования и измеренных (или желательных) кинематических данных. В контроллере 405 коррекции ошибок значение e_i ошибки умножается на позиционный коэффициент K_pi обратной связи, а значение

ошибки производной умножается на коэффициент K_vi обратной связи по скорости для формирования модифицированного ускорения

^°. Параметры K_pi и K_vi определяются в уравнениях 9 и 10 как постоянные диагональные матрицы, которые управляют уравнениями 1, 2 и 3.5 is a structural diagram of a tracking system for segment i, illustrating additional details of the error correction controller. In the illustrated embodiment, the error correction controller 405 comprises modules that implement Equation 8, where the parameter K _pi represents the positional feedback coefficient and the parameter K _{vi the} speed feedback coefficient. The difference module 510 is designed to generate the error value e _i (defined in equation 12) and the value

errors derived from kinematic data obtained as a result of modeling and measured (or desired) kinematic data. In the error correction controller 405, the error value e _i is multiplied by the feedback positional coefficient K _pi , and the value

the derivative error is multiplied by a velocity feedback coefficient K _vi to form a modified acceleration

^° . The parameters K _pi and K _{vi are} defined in equations 9 and 10 as constant diagonal matrices that control equations 1, 2 and 3.

, не учитывается в уравнении 8. Следовательно, в любом случае в системе слежения используется только модифицированное ускорение

^°. Преимущество неиспользования второй производной кинематических данных с наличием шума состоит в повышенной точности оценки силы и момента.To study the effect of turning on accelerations (a = 1) and eliminating accelerations (a = 0), a parameter was added during the simulation. It will be appreciated by those skilled in the art that when parameter a is set equal to zero, the second derivative of kinematic data, a member of the acceleration estimate

, is not taken into account in equation 8. Therefore, in any case, the tracking system uses only modified acceleration

^° . The advantage of not using the second derivative of kinematic data with noise is the increased accuracy of the force and moment estimates.

^° на суставе i с использованием варианта структуры обратной связи, описанного выше. Анализ обратной динамики выполняется на этапе 620 для получения и сил и момента на суставе i+1. В случае рекурсии, где i=1, сила реакции/момент на суставе 1 вводятся на этапе 620 как U₁. В других случаях рекурсии, где i≠1 и i+1<n, информация о нагрузке на сустав для сустава i+1 (представленная как конкатенированный вектор U_i+1) подается в качестве входных данных U₁ для следующего сегмента в другом случае рекурсии. U_i+1 вводится на этапе 625 в анализ прямой динамики для получения моделированных кинематических данных на суставе i. На этапе 630 определяется, требуется ли дополнительная рекурсия. Если i+1 равно n, то управление передается на этап 635, на котором рекурсия заканчивается, в противном случае значение i увеличивается на 1 на этапе 640 и управление возвращается на этап 605, на котором другой случай рекурсии выполняет процесс слежения для следующего сегмента тела.6 is a flowchart illustrating a recursive tracking process. The initial value of i is 1 for a series-connected system with the segment of interest n. As described above, n is the last segment of interest, i.e. recursion stopping point. The process starts at step 605. The measured or desired kinematic data for segment i is obtained at step 610. As described above, segment i has joints (joints), designated as i and i + 1. Then, at step 615, the modified acceleration is calculated

^° on joint i using the feedback structure option described above. An analysis of the inverse dynamics is performed at step 620 to obtain both the forces and the moment at the joint i + 1. In the case of recursion, where i = 1, the reaction force / moment at joint 1 is entered at step 620 as U ₁ . In other cases of recursion, where i ≠ 1 and i + 1 <n, the joint load information for the joint i + 1 (represented as a concatenated vector U _{i + 1} ) is supplied as input U ₁ for the next segment in another case of recursion . U _{i + 1} is introduced at step 625 into the direct dynamics analysis to obtain simulated kinematic data on the joint i. At step 630, it is determined whether additional recursion is required. If i + 1 is n, then control passes to step 635, where the recursion ends, otherwise the value of i increases by 1 at step 640, and control returns to step 605, in which another case of recursion performs the tracking process for the next segment of the body.

C. Direct forecasting of new movements

In one embodiment of the present invention, the dynamic equation of motion simulation provided by the forward dynamics module can be used to predict new movements. The simulated kinematic data represent segmental position and velocity data from the estimated joint load (including forces and moments). Thus, the direct dynamics module can be performed with the possibility of modeling new movements of body segments in response to the applied forces and moments.

You can change various parameters in a direct model and observe the effect on the simulated response. For example, a change in segment parameters such as mass, inertia, length and center of mass in direct dynamics module 415 affects the kinematic reaction. This type of prediction capability allows studying the sensitivity of the direct dynamics module 415 to physical parameters.

D. Error dynamics

The problem of estimating the rotation moment and joint strength is described in one embodiment of the invention as a tracking system using a non-linear feedback control law according to equation 6. To demonstrate the implementation of tracking, it is advisable to consider the dynamics of errors with a closed loop. In Fig. 5, the result U _{i + 1 of} the inverse dynamics module represents the control law according to Equation 6. If this control law is introduced into the direct dynamics module (by substituting in Equation 4), the relation for the closed loop according to Equation 11 is obtained. Equation 12 defines e _i as an error between the measured kinematic data q _mi and the simulated state variable q _i , which is obtained as a result of integration in the direct dynamics module 415. The error dynamics for several scenarios are described below.

Taking into account accelerations: a = 1

In an ideal situation with accurate measurements and zero error in the numerical differentiation, the dynamics of errors in a closed cycle are determined by differential equation 13.

The error dynamics of the state variable q _i can be controlled independently by assigning an eigenvalue. Let λ ₁ and λ ₂ denote the eigenvalues of equation 13. Equation 14 provides a critically decreasing solution, i.e. without sinusoidal oscillations, with real and equal eigenvalues. This solution provides the fastest and most accurate answer.

Equation 15 shows the relationship between K _p and K _v to achieve a critically diminishing response.

In one embodiment, the correct tracking and calculation time can be achieved using eigenvalues having a value of 100. Below, with reference to Figs. 8-23, simulation results with both large and low feedback coefficients will be described.

2. Excluding accelerations: a = 0

Suppose that the accelerations estimated from the measured kinematic data are not taken into account, i.e. a = 0. The dynamics of errors in a closed cycle is expressed by an inhomogeneous differential equation 16.

ограничен, ошибка сводится к нулю за счет присвоения собственным значениям в уравнении 16 отрицательной и вещественной части. Как и ранее, в случае с учетом ускорений, можно соответственно предусмотреть коэффициенты обратной связи для критически убывающего ответа с использованием отношения, данного в уравнении 15.Although the solution to equation 16 contains a coercive term, assuming that the acceleration term

is limited, the error is reduced to zero due to the assignment of eigenvalues in equation 16 of the negative and real parts. As before, in the case of accelerations, feedback coefficients can be provided for a critically decreasing response using the ratio given in equation 15.

3. Introduction of derivative estimation error

и член ускорения

можно точно вычислить путем дифференцирования кинематических данных. Действительно, ошибки численного дифференцирования содержащих шум кинематических измерений нельзя проигнорировать и они учитываются в следующих формулах.In the above formulations of equations for errors, it is assumed that the term of the derivative

and member acceleration

can be accurately calculated by differentiating kinematic data. Indeed, the errors in the numerical differentiation of noise-containing kinematic measurements cannot be ignored and they are taken into account in the following formulas.

и

выражены в уравнении 17:Let ε _υ and ε _η represent a limited error in the calculations of velocity and acceleration. Grades

and

expressed in equation 17:

Closed-loop dynamics, including the derivative estimation error, are given in equation 18.

Substituting equation 17 into equation 18, we obtain the following equation 19.

The error dynamics for a = 0 and a = 1 are given in equations 20 and 21.

E. Dynamics of a closed-form system

^° уравнения 23 определен в уравнении 24, в котором K_p и K_v являются диагональными матрицами n×n, имеющими критически убывающий отклик.In a further embodiment, the tracking system can be applied to closed-shape speakers. The equations of the closed-form system for an unbounded rigid body system are described by the number n of differential equations in the matrix form of equation 22. In equation 22, M corresponds to the mass matrix, and P corresponds to the contributions due to the terms of the Coriolis force, centrifugal force and gravity, respectively. The input U values correspond to the net moments of rotation of the joint. Like the described recursive variants, the control law according to equation 23 is used to linearize and separate the dynamics of the system. Member

^{° of} equation 23 is defined in equation 24, in which K _p and K _v are n × n diagonal matrices having a critically decreasing response.

F. Modeling a planar system with an open circuit

7 is a diagram of a free body illustrating a two-dimensional system with an open circuit containing three segments. These three segments include the shin 705, the thigh 710, and the trunk 715 of the person. It is believed that joint 710 is articulated to the base. The knee joint 725 connects the shin 705 and the hip 710. The hip joint 730 connects the hip 710 and the trunk 715. The simulation demonstrates the implementation of one version of the tracking system to evaluate the forces and moments of the joints. The selected system parameters are typical for an average man with a height of 1.7 m and a weight of 74 kg. The simulated movement under consideration is the squat movement in the ankle, knee and hip joints 720, 725 and 730. The goal is to use U ₁ as a constraint for initializing recursion and for iteratively calculating U ₂ = [F ₂ G ₂ τ ₂ ] and U ₃ = [F ₃ G ₃ τ ₃ ]. The required vector of moments and joint strength is denoted as U = [u ₁ u ₂ u ₃ ] ^T. For the development of reference trajectories, the registered movement of the average man performing a squat is used. Those skilled in the art will understand how motion can be recorded and recorded using conventional methods. The Newton-Euler equations for the motion of each isolated body segment are described in the following equations 25-33.

1. Segment 1: Shin 705

2. Segment 2: Hip 710

3. Segment 3: Torso 715

The simulation is intended to compare the performance of the tracking system with the traditional reverse dynamics approach. Input data includes kinematic data for motion, as well as support reaction forces. In the described simulation, the operation of the tracking system is analyzed for two cases: taking into account the estimates of acceleration (a = 1 in figure 5) and without taking into account the estimates of acceleration (a = 0 in figure 5). To ensure consistency, it is assumed that the measurements of the support reaction are ideal and obtained analytically. The analytically calculated vector U ₁ = [F ₁ G ₁ τ ₂ ] of the support reaction is obtained using the recursion equations, starting from the trunk 715 and moving towards the support, as described above. When using U ₁ as a constraint, U ₂ and U ₃ are recursively evaluated. Modeling is performed for two different sets of feedback coefficient matrices that give a critically decreasing response. The simulation results are shown in Figs.

In the simulations shown in Figs. As described above, the inclusion of acceleration estimates is often undesirable, because the analysis of the inverse dynamics requires the calculation of higher order derivatives, which leads to erroneous results. Each dashed curve in Figs. 8-11 corresponds to the accuracy of the simulated tracking, which does not take into account the desired accelerations (a = 0). On both graphs in FIGS. 8 and 9 and on the graphs of force and moment in FIGS. 10 and 11, excluding accelerations, the simulated result using small feedback coefficients gives unsatisfactory tracking characteristics. As shown in FIGS. 12-15, when the desired accelerations (a = 1) are turned on, extremely good tracking and joint moment characteristics are obtained.

In contrast to FIGS. 8-11, the models in FIGS. 16-19 give excellent tracking characteristics. In these models, the feedback coefficients are increased to improve the results when the desired accelerations are not taken into account (a = 0). Equations 35 and 36 give the parameters of the feedback coefficients. In both displacement graphs in FIGS. 16 and 17 and the force and moment graphs in FIGS. 18 and 19, the dashed lines representing the accuracy of the simulated tracking without taking into account the acceleration estimates (a = 0) practically do not differ from the reference data. As can be seen in the drawings, the options for evaluating the nonlinear feedback of the forces and moments of the joints are effective and do not require, for example, higher-order derivatives of noise containing measured data.

On Fig presents a graph illustrating the tracking error for the displacement of the ankle joint in Fig.7. The dashed line in the figure corresponds to the absolute value of the average tracking error when the desired accelerations are taken into account (a = 1). The solid line corresponds to the absolute value of the average tracking error when acceleration estimates are not taken into account (a = 0). For each of several values of K _p , the average tracking error (during simulation) between the desired and the simulated angle was calculated. For each data point, the absolute value of the average error was calculated to plot the graph. In the illustrated case, when acceleration estimates (a = 0) are not taken into account, the average tracking error for displacement of the ankle joint 720 tends to zero with increasing values of K _p . The average tracking errors for other angles and states are not shown specifically, as the specialist understands that this gives similar results.

The present invention can be implemented in many different forms, and should not be construed as limited to the described options. These options are presented solely for the thorough and complete disclosure of the invention, so that specialists can get a complete picture of it. For example, one skilled in the art will understand that the described tracking systems and methods can be extended to three-dimensional systems. In addition, in the module 415 direct dynamics (figure 4) you can enter, for example, conventional methods of distribution of muscle effort. The result of the muscle distribution module can then be used to initiate direct modeling. Alternatively, the muscle stress distribution module may use the result of the inverse dynamics module 410 (FIG. 4) and not be used in direct modeling.

In addition, the proposed device and methods are not limited to rigid bodies. Those skilled in the art will understand that the principles of the present invention can be applied to other systems that can be characterized by Equation 22. Evaluation options using feedback track data from systems controlled by a second-order differential of the data set.

Despite the described preferred assessment options using feedback of the forces and moments of the joints (which are illustrative and not restrictive), it should be noted that specialists will be able to propose modifications and changes based on the disclosure presented. Therefore, changes can be made to the specific embodiments described that fall within the scope of the claims described in the appended claims and equivalents.

Claims (37)

1. The method of determining the estimated joint load, which consists in obtaining at least one moment of rotation of the joint, obtaining kinematic data for the joint, calculating the modified acceleration using at least kinematic data, and determining the simulated kinematic data using the control law, moreover, the control law uses at least one moment of rotation of the joint. 2. The method according to claim 1, in which the control law uses at least a modified acceleration to linearize and separate the dynamics of the system. 3. The method according to claim 1, in which when calculating the modified acceleration, a feedback coefficient is additionally used to determine the modified acceleration. 4. A method for determining the estimated joint load, which consists in obtaining kinematic data for the joint, receiving input force for the joint, calculating the modified acceleration using at least kinematic data, performing an analysis of the inverse dynamics to obtain the estimated joint load, reverse dynamics analysis uses at least modified acceleration and input force, and performs direct dynamics analysis on the estimated joint load to determine the simulated kinematic data for the joint. 5. The method according to claim 4, in which the coordinates of the center of mass and the angle of the joint are used as kinematic data. 6. The method according to claim 4, in which the support reaction force is used as the input force. 7. The method according to claim 6, in which the joint of interest is additionally determined, starting from the support reaction force, the load on the adjacent joint is evaluated and the evaluation is repeated until the adjacent joint is the joint of interest. 8. The method according to claim 4, in which as the input force use the measurement of the plane of force. 9. The method according to claim 4, in which the input force is zero. 10. The method according to claim 4, in which the input force acts at the point of contact on the segment connected to the joint. 11. The method according to claim 4, in which at least one of: internal force and internal moment is used as the input force. 12. The method according to claim 4, in which as the input force use the moment of rotation of the joint. 13. The method according to claim 4, in which when calculating the modified acceleration, an error value is further calculated representing the difference between the simulated kinematic data and the measured kinematic data, and a feedback coefficient is applied to the error value. 14. The method according to item 13, in which at least one coefficient is used as a feedback coefficient from a positional feedback coefficient and a speed feedback coefficient. 15. The method according to claim 4, in which when performing the analysis of direct dynamics additionally perform the integration of the estimated load on the joint. 16. The method according to claim 4, in which additionally use the feedback of the simulated kinematic data in calculating the modified acceleration. 17. The method according to claim 4, in which additionally use the feedback of the simulated kinematic data when performing the analysis of the inverse dynamics. 18. The method according to claim 4, in which additionally use the feedback of the simulated kinematic data when performing the analysis of direct dynamics. 19. The method according to claim 4, in which additionally obtain kinematic data for the second joint, calculate the second modified acceleration using at least kinematic data for the second joint, perform an analysis of the inverse dynamics to obtain a second estimated load on the joint, and in the analysis of the inverse dynamics use at least a second modified acceleration and estimated joint load, and perform direct dynamics analysis on the second estimated joint load to obtain simulated kinematic data for the second joint. 20. A device for determining an estimated joint load containing an error correction controller for calculating a modified acceleration using at least kinematic data, an inverse dynamics module including an input force for determining an estimated joint load using at least a modified acceleration both the input force and the direct dynamics module, designed to determine the simulated kinematic data for the joint using at least the least estimated joint load. 21. The device according to claim 20, in which the error correction controller comprises a difference module for generating error values from the simulated kinematic data and kinematic data, wherein the error correction controller is designed to calculate the modified acceleration using the feedback coefficient to the error value. 22. The device according to item 21, in which at least one coefficient is used as a feedback coefficient from a positional feedback coefficient and a speed feedback coefficient. 23. The device according to claim 20, in which the estimated joint load in the case of the first recursion is related to the value of the input force for the second case of recursion. 24. The device according to claim 20, in which the error correction controller is configured to receive the simulated kinematic data as feedback. 25. The device according to claim 20, in which the reverse dynamics module is configured to receive the simulated kinematic data as feedback. 26. The device according to claim 20, in which the direct dynamics module is configured to receive simulated kinematic data as feedback. 27. The device according to claim 20, in which the direct dynamics module is configured to integrate the estimated joint load to determine simulated kinematic data. 28. The device according to claim 20, in which the reaction force of the support is used as the input force. 29. The device according to claim 20, in which the measurement of the plane of force is used as the input force. 30. The device according to claim 20, in which the input force is zero. 31. The device according to claim 20, in which the input force acts at the point of contact on the segment. 32. The device according to claim 20, in which at least one parameter of: internal force and internal moment is used as an input force. 33. The device according to claim 20, in which the moment of rotation of the joint is used as the input force. 34. The device according to claim 20, characterized in that it uses a software product on a computer-readable medium. 35. A computer-readable medium containing program instructions for obtaining kinematic data for a joint, program instructions for obtaining input force for a joint, program instructions for calculating modified acceleration using at least kinematic data, program instructions for performing inverse dynamics analysis to obtain an estimated load on the joint, and at least a modified acceleration and input force, and program commands to execute analysis of direct dynamics over the estimated load on the joint to determine the simulated kinematic data for the joint. 36. The computer-readable medium of claim 35, comprising program instructions for calculating an error value representing a difference between simulated kinematic data and kinematic data, and program instructions for applying a feedback coefficient to the error value. Priority on points: 06/19/2001 according to claims 1-36.

Images