Method for estimating forces and moments using feedback

Reference to Related Applications

The present application is related to provisional patent application US №60 / 301891, filed June 29, 2001, for the invention "A recursive method using nonlinear feedback to evaluate the forces and moments on joints based kineziologicheskuyu measurements" and provisional US patent application number 60/353378, filed January 31, 2002 for the invention of "Direct address inverse dynamics: feedback linearization method", under which claims priority under 35 USC § par.119 position (a).

A. Field of the Invention

The present invention relates to the analysis of human movement, in particular to the analysis of the forces and moments of the joints using a non-linear feedback in direct modeling of the dynamics.

B. Description of the prior art

In the study of human motion to assess the forces and moments of the joints commonly used analysis of reverse (inverse) speakers. In conventional inverse dynamics analysis of the forces and moments of the joints are calculated from observations of segmental motion. Inverse dynamics analysis is commonly used in solving problems of biomechanics, as the internal forces of human joints can not be measured in a simple manner. However, you can measure the segmental motion and bring the corners of the joints of the measured displacement to determine the forces and moments of the affected joints.

One problem with the use of inverse dynamics in the study of human movement is the emergence of error caused by calculation of higher order derivatives to determine the forces and moments of the joints. Methods of using the concept of inverse dynamics in biomechanics work well if the input signals do not contain the noise, the dynamic model is flawless. However, experimental observations are imperfect and contain noise. The sources of noise are as a measuring device, and the joint itself. Methods of inverse dynamics to calculate joint moments require the computation of higher order derivatives based on experimental observations. In particular, a member of the angular acceleration is the second derivative of the joint angle, and the linear acceleration is the second derivative of the acceleration of the center of mass. Numerical differentiation experimental observations increases the noise. Of particular importance for the solution of problems calculate velocities and accelerations is the availability of high-frequency noise. The amplitude of each of the harmonics increases with its harmonic number: rate increases linearly as the acceleration increases in proportion to the square of the harmonic number. For example, the second order differentiation signal ω rf noise may result in a signal with frequency components ω2. As a result of the parabolic noise gain obtained erroneous calculation of forces and joint moments.

Although there are methods of noise filtering, such filtering is complicated to implement and requires a lot of time because it requires a large analysis to separate the true signal from noise biomechanical data. For example, to reduce the high-frequency error is commonly used low-pass filtering. However, the complexity of the lowpass filter is to select an optimal cutoff frequency fc. As a general solution for selecting optimal filter parameters does not exist, the results of filtering methods are often unreliable.

To evaluate the forces and joint moments without errors resulting from the implementation of conventional inverse dynamics analysis were proposed approaches based optimization. Unlike inverse dynamics based on optimization techniques do not require numerical differentiation. However, the use of solutions based on the optimization is limited, because these methods require computationally expensive, do not guarantee convergence and usually very difficult to implement.

Another problem associated with using inverse dynamics to analyze the movements of the person, is that the method does not inverse predictive nature of new movements. When inverse dynamic forces and moments are calculated from the observed responses. Prediction of new movements requires the calculation of the reaction to be expected as a result of the application of forces and moments. Analysis of inverse dynamics makes it impossible to predict, as calculated forces and moments, and not a reaction, expected as a result of the application of forces and moments.

Thus, a need exists for efficient computationally system and method that: (1) able to evaluate the forces and moments joints without errors due to higher-order derivatives; (2) do not require a closed analyzing the entire body in a closed form; and (3) make it possible to predict the nature of human movement.

SUMMARY OF THE INVENTION

One embodiment of the present invention enables to estimate the load on the human joints. The load on the joint comprises the forces and moments acting on the joint. The module defines the dynamics of the direct kinematic data by numerical integration (or simulation) of dynamic equations of motion. Controller error correction eliminates the tracking error between the kinematic data obtained from direct modeling, and measurement (or desirable) kinematic data. The controller generates the modified error correction acceleration input module inverse dynamics. In one embodiment, the modified acceleration value is determined without regard to the second derivative of the measured (or desired) kinematic data. Thus, the estimated load on the joints when it is inserted into the module monitors the dynamics of direct measurements (or desirable) kinematic data without errors related to the calculation of higher order derivatives "noisy" kinematic data.

In another embodiment, the load on the joints are evaluated recursively plane sequentially coupled system. Recursive method, the process starts at the first end segments of the series circuit and the load on the joints are calculated toward the second end of the series circuit. The segments of the chain are interconnected by joints, and the forces and moments in a joint reactions are common to two interconnected segments. Loads on the joints, estimated for the first segment used in the evaluation for the next segment until until it reaches the interested joint or joints. This means that the result is the recursive calculation of forces and moments at the connection point for the next segment. This result is used as input (input data) for analysis of the next segment. Consequently, the recursive method does not require modeling of the dynamics of the body. While in any particular case may require recursive modeling the dynamics of all the body, however, the recursive technique provides flexibility, which allows to reduce the sources of error.

Recursive estimation options include an open (non-closed) circuit and evaluation of the closed (closed) circuit. The system is limited to open-chain medium at one end, while the other free terminal segments. In a system with more than one closed chain end is in contact with the environment. Segments of the communication system are numbered in order of recursion from segment 1 to segment n, which is the last considered segment. Segment n is not necessarily to be in the last segment of a plurality of bodies. Rather, for the segment n have the segment where it is desirable to stop the recursive computation, as all forces and moments of interest are already found. To initiate recursion, you must have the power and torque acting on the first segment. For example, when analyzing human movement generally measured base reaction force (floor reaction) in the way, that initialize a recursive equation. Using the reaction forces increases the accuracy of estimates of stress on the joints, which are in close proximity to the substrate.

In another embodiment, the tracking system according to the invention can be applied to the dynamics of the closed form. The equations of a closed form for a system of unlimited rigid body are described by n differential equations. Like the embodiments described using recursion is used for linearization control law and separation (the outbreak) the dynamics of the system.

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

BRIEF DESCRIPTION OF DRAWINGS

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

1 illustrates how to use a recursive computation for separating the dynamics of the lower body of the dynamics of the upper body,

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

3 is a free body diagram for a segment sequentially coupled system,

Figure 4 shows a block diagram of a tracking system for communication segment i,

5 is a block diagram of a tracking system for segment i connection, illustrated in more detail the error correction controller,

6 is a flowchart illustrating a process of recursive tracking

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

8A-8C are graphs illustrating tracking accuracy for the displacement of the ankle joint of Figure 7 using a low feedback gain and without accelerations

9A-9C are graphs illustrating tracking accuracy for the displacement of the knee joint of Figure 7 using a low feedback gain and without accelerations

10A-10C are graphs illustrating tracking accuracy for the forces and moments on the knee joint 7 with small feedback gain and without accelerations

11A-11C are graphs illustrating tracking accuracy for the forces and moments of the hip joint of Figure 7 using a low feedback gain and without accelerations

12A-12C are graphs illustrating tracking accuracy for the displacement of the ankle joint of Figure 7 using a low feedback gain and subject accelerations

13A-13C are graphs illustrating tracking accuracy for the displacement of the knee joint of Figure 7 using a low feedback gain and subject accelerations

14A to 14C are graphs illustrating tracking accuracy for the forces and moments on the knee joint 7 with small feedback gain and subject accelerations

15A to 15C are graphs illustrating tracking accuracy for the forces and moments of the hip joint of Figure 7 using a low feedback gain and subject accelerations

16A to 16C are graphs illustrating tracking accuracy for the displacement of the ankle joint of Figure 7 using large feedback gain and without accelerations

17A to 17C are graphs illustrating tracking accuracy for the displacement of the knee joint 7 by using large feedback gain and without accelerations

18A-18C are graphs illustrating tracking accuracy for the forces and moments on the knee joint 7 by using large feedback gain and without accelerations

19A-19C are graphs illustrating tracking accuracy for the forces and moments of the hip joint of Figure 7 using large feedback gain and without accelerations

20A to 20C are graphs illustrating tracking accuracy for the displacement of the ankle joint of Figure 7 using large feedback gain and subject accelerations

21A-21C are graphs illustrating tracking accuracy for the displacement of the knee joint 7 by using large feedback gain and subject accelerations

22A-22C are graphs illustrating tracking accuracy for the forces and moments on the knee joint 7 by using large feedback gain and subject accelerations

23A-23C are graphs illustrating tracking accuracy for the forces and moments of the hip joint of Figure 7 using large feedback gain and subject accelerations

Figure 24 is a graph showing error to bias ankle 7.

DESCRIPTION OF PREFERRED EMBODIMENTS

Below are described preferred embodiments with reference to the accompanying drawings, in which like reference numerals refer to identical or functionally similar elements. Also, left-most digit of each reference number corresponds to the figure in the figures, in which this number was used for the first time.

Figure 1 is an illustration showing how the recursive computation is used to separate the lower body dynamics of the dynamics of the upper body. Illustration 105 shows the upper part of the body and a lower body portion 110. One segment of the upper body portion 105 is shown with a load 140. The lower body portion 110 includes segments 120 having an ankle joint, the knee joint and the hip joint 125 130. When recursive method to compute the forces and joint moments upper portion 105 of the body can be modeled separately from the bottom 110 body. Since counter 115 forces the base (floor reaction) can effectively insulate the joints 120, 125 and 130 of the lower body portion 110, as well as related communication parameters segments from the upper portion 105 of the body. This means that internal forces and moments acting on the joints 120, 125 and 130 can be evaluated without the effects due to the load 140 and the physical parameters of the upper portion 106 of the body, such as weight, center of mass, inertia, and the length of the segment. These parametric uncertainty of the upper portion 105 of the body are important sources of errors in the evaluation of internal forces and moments in the human body when using the procedure of the dynamics of the whole body in a closed form. In contrast to the solutions in a closed form for the whole body, in embodiments of recursive solutions are used measuring forces 115 floor reaction as constraints for the recursive calculation of the moments of the joints, starting from the base (support) and moving up, for example, the knee joint 125 and hip joint 130 .

Using recursive method to evaluate the forces and moments of the joints allows to focus on the interests of the joints without additional sources of error. In addition, the recursive method measuring floor reaction forces 115 as input provides, for example, additional measurement modality. That is information on the association of the kinematics and the reaction force provides an additional opportunity to improve the reliability of the estimates of the internal forces. A person may be exposed to stresses or constraints unpredictable dynamics of the interaction with other objects or other persons in the environment. Such circumstances may change the dynamic performance required to evaluate internal forces and moments in the joints. Some applications for the use of recursive method in these circumstances include biomechanical research and development tasks lifting control assistive devices that help people with disabilities in carrying out their daily tasks. Skilled understood that to provide additional modalities of perception, for use in the assessment of the various forces and moments, can serve as force and pressure sensors built into the shoes.

A recursive method for the two-dimensional system with a series circuit

Embodiments of the present invention are applicable to planar systems including recursive and recursive open circuit closed circuit. In a system with maximum open circuit one end of a system consisting of a plurality of bodies in contact with the environment. Another end or ends are free or limited. In a system with more than one closed chain end is in contact with the environment.

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

For each of the joints 220, 222, 224 and 226 are shown torques joints, horizontal and vertical reaction force of the reaction force of each joint, designated as τI, Fi and Gi, respectively. For example, the first joint 220 illustrated torque τI, horizontal reaction force Fi and the vertical force reaction Gi. The following describes an example of recursive calculation with reference to Figure 2. When the recursive computation system of a plurality of bodies conceptually divided into individual segments. We analyze free body diagram of each segment. Segments interconnected by joints (hinges), for example a second joint 222. The reaction forces and moments, such as the second joint 222, are common to the first segment 205 and second segment 210. The analysis begins with the first segment 205, and the calculated force and moment in the connection point of the second segment 210, ie, the second joint 222 (the hinge). The calculated force and moment of the second joint 222 are the result of the recursion 1. This result is used as input for the analysis of the next segment, such as segment 210. The second segment analysis continues recursively until until it reaches the n-th segment 215. This n th segment 215 of interest is the segment or segments to which it is desired to stop the recursive computation. In the embodiment where the first segment 205 are floor reaction force 115 (1), the force and the moment acting on the second joint 222, calculated based on the forces and moments acting on the first joint 220. Then calculate the forces and moments acting on the a third joint 224, on the basis of the previously calculated forces and moments acting on the second joint 222. This recursive procedure using dynamic calculation result as input data for the next calculation is repeated until, until we find the forces and moments of interest for the joint or joints . Skilled person will appreciate that the n-th segment 215 is not necessarily the last segment in the plurality of bodies. Rather, for the n-th segment it is meant the segment where it is desirable to stop the recursive computation, because it will already be found interesting forces and moments. It should also be noted that the floor reaction force 115 acting at the contact point, which is not necessarily located at the joint. Further details of these calculations will be described below with reference to Figure 3.

3 shows a free body diagram for a segment sequentially coupled system. Segment 305 represents the i-th segment planar sequentially related systems, such as the system illustrated in Figure 2. Segment i joint body comprises i (310) and the joint i + 1 (315). For an isolated segment i, where i = 1 ... n, the acceleration of the center of gravity is denoted as (), the angle of the joint relative to the vertical - θi and angular acceleration -. As shown in Figure 3, the physical parameters for the segment i of the body include: mass mi, the moment of inertia Ii, segment length Li and a length ki to the mass center. Also in Figure 3 for each joint 310 and 315 shown moments τi rotation joints, the horizontal reaction force Fi and Gi vertical reaction forces. The following are the Euler-Newton equation to calculate the forces and torques on each of the joints 310 and 315 of the body segment i in equations 1, 2 and 3.

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Those of skill recognize that equation 1 is the expression for adding the forces acting on the body segment 305 in the projection on the x axis or horizontal direction. Similarly, Equation 2 is an expression for combining the forces acting on the body segment 305 in the projection on the y-axis or vertical direction. In equation (2) g denotes gravitational acceleration. Equation 3 is an expression for the addition of angular accelerations acting on the joints 310 and 315.

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In inverse dynamics analysis of the forces and moments acting on the joints, are calculated from the measured or desired kinematic data. The kinematic data comprises center of mass coordinates and a joint angle data. In one embodiment, a recursive solution to calculate the forces and moments at each joint can be obtained from the compact representation (in a matrix), the Newton-Euler equations in Equation 4 shown below. In Equation (4) Ui = [Fi Gi τI] T - vector (transposed) whose elements correspond to the horizontal force, the vertical force and torque, respectively, applicable to the joint i (310). Forces and moments on the joint i + 1 (315) are described as Ui + 1. Other details of the recursive solutions for Ui and Ui + 1 will be described below.

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Vector qi = [xi y θI] T represents the coordinates of the center of mass and the angle of the joint for the joint i. Those of skill recognize that term in Equation 4 is the second derivative of the vector qi. Elements of equation 4 in more detail are defined as follows:

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2. Evaluation of open-chain

As described above, the open-chain has one end in contact with the environment. The end in contact with the environment, called "limited end". In one embodiment of the present invention are limited human leg end in contact with the ground or other supporting surface. In one embodiment, the kinematic data are supplemented by measurements floor reaction force 115 (indicated as U1) to improve the accuracy grade inertial forces and moments. The segments are numbered in the direction from the bottom upwards, from 1 to n, where n - the last segment under consideration. Thus, in the method of the inverse dynamics of the Newton-Euler used measure forces and moments underfoot. When U1, used as a boundary condition on the segment 1, the force and moment on the segment i, where i is an integer from 1 to n (i: 1 → n), are computed sequentially by Equation 5, since the segment 1 and advancing the segment n. When evaluating the open-chain, where n is the last segment in the chain, there are no external forces acting on the n, so that Un + 1 = 0.

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Because there are biomechanical model noise and measurement errors, the boundary condition at the free segment is usually broken. In other words, in the embodiment, with (open loop) circuit, where the recursion goes from one segment to the free segment (denoted by n), Un + 1 is not equal to 0. This excess deterministic allowed by addition of the residual forces and torques to a segment n. The advantage of a recursive formulation of the segments with the numbering from 1 to n is that there is no need to model the entire body. Evaluation of force and torque on the end segment n regardless of whether it is the last segment of the serial system or not. Parametric uncertainty for the upper extremities, and the uncertainty in the model of rigid body are important sources of error in the assessment of internal forces and moments. However, these uncertainties upper limb can be avoided only when required moments joints closest to the plane of force.

In another embodiment, open-chain kinematic measurements are only available. Segments are numbered from 1 to n, where segment 1 has a free end, but not limited to the end. Since one segment having a free end, U1 = 0 is the boundary condition for the recursion towards the segment n.

3. Evaluation of the closed circuit

In another embodiment, the estimate with the closed circuit. As described above, the closed-loop system has more than one end in contact with the environment. In this embodiment, for evaluation of internal forces and moments required measurement sensors or other source of power. Segments are numbered consecutively from segment 1 to segment n, which is the last segment of interest. The measurement data for the sensor or the initial force on the segment 1 is denoted as U1, where U1 ≠ 0 because the end of one segment is limited. In measurements U1, available as a boundary condition on the segment 1, the force and moment on the segment i, where i is an integer from 1 to n (i: 1 → n), are computed sequentially by Equation 5, since the segment 1 and moving to segment n.

<img he="7" wi="70" file="00000021.tif" img-content="undefined" img-format="tif" />

4 is a block diagram of a tracking system for segment i body. Controller 405 error correction unit 410 inverse dynamics module 415 direct speakers are connected and form a tracking system. Inputs to the controller 405 an error correction include kinematic data and variables as well as the status and qi. In one embodiment, measurement is required or desired kinematic data (), and evaluation of their velocity (). Ratings acceleration () can be used in applications that do not contain the noise, but they are not necessary. The controller 405 outputs the error correction acceleration ° modified as input for the inverse dynamics module 410. Inverse dynamics module 410 has additional inputs Ui and qi. Vector Ui represents the forces and moments at the joint i. Output module 410 inverse dynamics are estimates Ui + 1 power and torque for the joint i + 1,. Input module 415 415 direct speakers include Ui, Ui + 1 and qi. Furthermore, an estimated force and moment joint Ui + 1 is used as input data during the next iteration, where they are indicated as Ui increments i. In each case, the iteration or recursion Ui is the input data, and Ui + 1 - the result. The module 415 provides direct dynamics variables qi and status. Parameters for the module direct the dynamics (ie Ai, Mi, Bi and Pi) are identical to the parameters for the inverse dynamics.

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In one embodiment, the joint forces and moments estimated using inverse dynamics module 410. Equation 6 is the inverse dynamics control law for the recursive calculation of the data load on the joint to Ui + 1 using the modified acceleration °. The module 415 calculates the dynamics of direct acceleration according to equation 7, and then performs numerical integration acceleration for variables qi and conditions relating to joint i. ECC controller 405 uses feedback variables qi and condition for forming a modified acceleration In one embodiment, the modified acceleration value is calculated without taking into account the second derivative of the measured or desired data kinematics. Error correction controller 405 generates the modified acceleration member such that the inverse dynamics module 410 calculates a set of input data or control data designated as the Ui + 1, which when entering in direct dynamics module 415 sequentially reproduced track or measured or desired kinematic data.

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Those of skill recognize that the described equation, expression, or function modules can be implemented in general-purpose computer or special purpose computer hardware. In one embodiment, the essential features of the invention are realized purpose computer that is programmed by special software. This software is preferably distributed in a computer readable medium that includes program instructions. Computer readable media can be, for example, is read out of memory. These volumes readable memory can be obtained by computing the public network, personal area network or the Internet. It is understood that the program instructions may be implemented in any suitable form, such as source code, object code or scripts.

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To study the effect of inclusion of accelerations (a = 1) and the elimination of accelerations (a = 0) during a simulation parameter is added. Those skilled understood that when a parameter is set to zero and the second derivative of kinematic data, the acceleration term evaluation is not considered in equation 8. Consequently, in either case, the tracking system is used only modified acceleration °. The advantage of not using the second derivative of kinematic data to the presence of noise is increased estimation accuracy and torque forces.

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In one embodiment, the simulation of the dynamic equations of motion, is provided by the direct dynamics can be used to predict the new movements. The simulated kinematic data are the data of the segmental position and velocity from the estimated load on the joint (including forces and moments). Thus, direct dynamics module can be adapted to model new movements of body segments in response to applied forces and moments.

You can change various settings in the direct model and observe the effect on the simulated response. For example, changing parameters such segments as mass, inertia, and the length of the center of mass of the module 415 direct impact on the dynamics of kinematic response. This type of predictive capability allows us to study the sensitivity of the module 415 to direct the dynamics of the physical parameters.

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The problem of evaluating the torque and power of the joints is described in one embodiment as a tracking system that uses a control law with nonlinear feedback according to the equation 6. For the demonstration of the tracking error is useful to consider the dynamics of the closed loop. 5 is the result of Ui + 1 module is inverse dynamics control law by the equation 6. If this law is put into the control module of the direct dynamics (by substituting in the equation 4), turns ratio for a closed cycle in accordance with equation 11. Equation 12 determines the ei as an error between the measured kinematic data qmi and simulate variable qi state, which is obtained by integrating the module 415 direct speakers. The following describes the dynamics of errors for multiple scenarios.

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In an ideal situation, with the exact measurements and zero error in numerical differentiation dynamics of errors in a closed loop defined by the differential equation 13.

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The dynamics of the variable qi error condition can be controlled independently by assigning your own values. Let λ1 and λ2 denote the eigenvalues ​​of the equation 13. Equation 14 provides a critical solution decreases, ie, without sinusoidal oscillations, with real and equal eigenvalues. This solution provides the fastest and most accurate answer.

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Equation 15 shows the relationship between Kp and Kv to achieve critical decreasing response.

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2. Without acceleration: a = 0

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Although the solution contains 16 compelling a member, assuming that the term is limited to the acceleration, the error is reduced to zero due to the assignment of the eigenvalues ​​in the equation 16, and a negative real part. As above, in the case of considering accelerations can respectively provide feedback factors critical for decreasing the response using the relationship given in equation 15.

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3. Introduction of the estimation error of the derivative