JP7281138B2 - Swing analysis device - Google Patents

Description

The present invention relates to a swing analysis device, method, and program for analyzing a swing of a hitting tool such as a golf swing.

A swing of a hitting tool by a player is a complex motion including various behaviors. For example, a golf swing is an action that combines various actions such as arm swing-up and swing-down, hip rotation, and body translation. Non-Patent Documents 1 and 2 disclose a method of decomposing a golf swing into a plurality of behaviors (modes) by singular value decomposition of an observation matrix obtained from measurement data obtained by measuring the golf swing.

Kenta Matsumoto, 5 others, ``Motion Analysis of Golf Swing by Singular Value Decomposition for Club Design'', Design Engineering, Vol. 53, No. 6, pp. 447-462, June 2018 Hiroshi Hatanaka, 4 others, ``Evaluation of impact on club characteristics based on analysis of motion of golf swing'', No. 18-15 The Japan Society of Mechanical Engineers Symposium: Sports Engineering and Human Dynamics 2018 Proceedings, B-10, November 2018

According to the methods of Non-Patent Documents 1 and 2, various behaviors that constitute a golf swing can be individually evaluated. However, such attempts have just started, and further improvements in analysis techniques are desired. The same applies to the analysis of swings of hitting tools other than golf clubs, such as tennis rackets and baseball bats.

An object of the present invention is to provide a swing analysis device, method, and program capable of estimating new behaviors based on individual behaviors included in the swing of a hitting tool.

A swing analysis device according to a first aspect includes a data acquisition unit that acquires time-series behavior data representing the behavior of a plurality of points of interest when a player swings a hitting tool in time-series, and singular value decomposition of the time-series behavior data. and a mode expansion unit that decomposes the behavior by doing so. The mode expansion unit extracts a plurality of characteristic behaviors respectively corresponding to a plurality of modes from the behavior by singular value decomposition of the time-series behavior data, and extracts at least one of the plurality of modes of interest. Modifying a first basis representing an excitation pattern of the behavior of the plurality of points of interest constituting the characteristic behavior corresponding to the mode, and determining the mode of interest based on the modified first basis Reconfigure the corresponding characteristic behavior.

A swing analysis device pertaining to a second aspect is the swing analysis device pertaining to the first aspect, wherein the mode expansion unit converts a plurality of components respectively corresponding to behaviors of the plurality of attention points included in the first basis. At least one component value is modified.

A swing analysis device according to a third aspect is the swing analysis device according to the second aspect, wherein the mode development unit selects at least one of the plurality of modes to be corrected according to an input from the user. At least one of a mode, at least one target component whose value is to be modified among the plurality of components, and a modification amount of the target component is determined.

A swing analysis device according to a fourth aspect is the swing analysis device according to the first aspect, wherein the mode development unit converts the first base of the mode of interest to a different mode from the mode of interest among the plurality of modes. together with the first basis of the paired mode of , about an axis orthogonal to the first basis of the mode of interest and the first basis of the paired mode.

A swing analysis device according to a fifth aspect is the swing analysis device according to the fourth aspect, wherein the mode development unit, among the plurality of modes, for each of a plurality of candidate modes different from the attention mode, , around an axis orthogonal to the first basis of the mode of interest and the first basis of the candidate mode such that the first basis of the mode of interest approaches a target value Rotate and select, as the pair mode, the candidate mode that gives the rotation that maximizes the correlation coefficient between the first basis of the attention mode after the rotation and the target value.

A swing analysis device according to a sixth aspect is the swing analysis device according to the fourth aspect, wherein the mode expansion unit includes a term representing an error between the first basis of the attention mode after rotation and its target value. A rotation angle is calculated that minimizes the error function comprising, and the first basis of the mode of interest is modified together with the first basis of the pair mode by rotating about the axis by the rotation angle.

A swing analysis device according to a seventh aspect is the swing analysis device according to the sixth aspect, wherein the error function further includes a term representing an error between the first basis of the pair mode after rotation and its target value. include.

A swing analysis device according to an eighth aspect is the swing analysis device according to any one of the first aspect to the seventh aspect, wherein the time-series behavior data includes positions, postures, velocities, accelerations, Data representing at least one of angular velocity, angular acceleration, force, and torque in time series.

A swing analysis device according to a ninth aspect is the swing analysis device according to any one of the first aspect to the eighth aspect, wherein the hitting tool is a golf club.

A swing analysis method according to a tenth aspect includes the following. A swing analysis program according to an eleventh aspect causes a computer to execute the following.
Acquisition of time-series behavior data representing the behavior of a plurality of points of interest when a player swings a hitting tool in time series. Decomposition of the behavior by singular value decomposition of the time-series behavior data.

Decomposing the behavior includes:
- Extracting a plurality of characteristic behaviors respectively corresponding to a plurality of modes from the behavior by singular value decomposition of the time-series behavior data - Corresponding to at least one mode of interest among the plurality of modes Modifying a first basis that constitutes the characteristic behavior and is a basis that represents an excitation pattern of the behavior of the plurality of points of interest; and based on the modified first basis, the corresponding mode of interest. Reconstructing characteristic behavior

According to the above viewpoints, new behaviors can be estimated based on individual behaviors included in the swing of the hitting tool.

1 is a functional block diagram showing the overall configuration of a swing analysis system including a swing analysis device according to a first embodiment of the present invention; FIG. FIG. 2 shows the location of markers attached to a golfer's body; 4 is a flowchart showing the flow of a swing analysis method according to the first embodiment; (A) Stick diagram representing the time average of time-series behavior data. (B) Stick diagram representing temporal averages of pseudo-extension data. FIG. 4 is a conceptual diagram showing the relationship between time-series behavior data and pseudo-extended data; Stick diagram of the first mode of 25 observation points. FIG. 4 is a comparative diagram comparing stick diagrams of each mode at the timing of impact between different golf swings by the same golfer. FIG. 4 is a comparative diagram comparing stick diagrams of each mode at the timing of impact between golf swings by different golfers. FIG. 4 is a flowchart showing sub-steps of step S8 of estimating a new behavior included in the flowchart of FIG. 3 according to the first embodiment; FIG. Graph of the components of the right singular vector (first basis). Graph of the components of the left singular vector (second basis). FIG. 4 is a stick diagram showing the behavior after correction of the right singular vector according to the first embodiment; Another stick diagram showing the behavior of the right singular vector after correction according to the first embodiment. FIG. 4 is a flow chart showing sub-steps of step S8 of estimating new behavior included in the flow chart of FIG. 3 according to the second embodiment of the present invention; FIG. FIG. 4 is an image diagram showing conversion of a right singular vector according to the first embodiment; FIG. 9 is an image diagram showing conversion of right singular vectors according to the second embodiment; FIG. 11 is a stick diagram showing the behavior after correction of the right singular vector according to the second embodiment; A stick diagram of the first mode of 53 observation points created from the same measurement data as in FIG. 6 (reference diagram). The conceptual diagram showing the relationship between the time-series behavior data and pseudo extended data which concerns on a modification. FIG. 11 is a conceptual diagram showing the relationship between time-series behavior data and pseudo-extended data when the average behavior according to another modified example is brought closer to the behavior at the time of impact. FIG. 4 is a flow chart showing sub-steps of step S8 of estimating a new behavior included in the flow chart of FIG. 3 according to the third embodiment of the present invention; FIG.

Hereinafter, swing analysis devices, methods, and programs according to some embodiments of the present invention will be described with reference to the drawings.

<1. First Embodiment>
<1-1. Overview of Swing Analysis System>
FIG. 1 shows an overall configuration diagram of a swing analysis system 100 including the swing analysis device 1 according to the first embodiment. The swing analysis system 100 is a system for analyzing golf swings. A golf swing is a complex action including various actions, and is configured by combining various actions such as swinging up and down of the arm, rotation of the waist, and parallel movement of the body. The swing analysis system 100 individually evaluates such characteristic behaviors included in the golf swing so that the characteristics of the golf swing can be captured more accurately. More specifically, the golf swing is decomposed into characteristic behaviors by performing mode expansion using singular value decomposition on time-series behavior data representing the behavior of a golfer when he swings a golf club in time series. Based on the results of singular value decomposition described above, the user can understand the characteristic behaviors included in the golf swing, and in turn understand the characteristics of the golfer, the characteristics of the golf club, and the like. The user here is a general term for a person who needs the results of golf swing analysis, such as a golfer himself or his instructor, a fitter who fits a golf club suitable for a golfer, or a golf club developer. .

Time-series behavior data to be subjected to singular value decomposition is acquired based on measurement data measured by the measuring device 2 . The measuring device 2 constitutes a swing analysis system 100 together with the swing analysis device 1 . Hereinafter, after explaining the configuration of each part of the swing analysis system 100, the swing analysis method by the swing analysis system 100 will be explained.

<1-2. Details of each part>
<1-2-1. Measuring equipment>
A measuring device 2 according to the present embodiment is a motion capture system including a plurality of cameras 21, 21, . As a motion capture system, for example, a three-dimensional motion analysis system manufactured by VICON can be preferably used. A plurality of cameras 21, 21, . .

In this embodiment, markers are attached to positions of observation points on the golfer's body so that the cameras 21, 21, . . . More specifically, as shown in FIG. 2, I ₀ pieces (in this embodiment, I ₀ ≧3 and in particular I ₀ =53), light-reflecting spherical markers 20, 20, . . . are attached. In this example, the markers 20 , 20 , . . . are attached to the bodysuit worn by the golfer 7 .

The cameras 21, 21, . . . continuously photograph the situation at a predetermined sampling frequency while the golfer 7 makes a golf swing using the golf club. The sampling frequency can be, for example, 500 Hz. In the present embodiment, the golf swing is measured at least during the period from address, back at 9 o'clock, top, down at 9 o'clock, impact, follow-up at 3 o'clock in order until the finish. Here, 9 o'clock back is the timing when the golf club points in the 9 o'clock direction during the backswing when the golfer 7 is viewed from the front, and 9 o'clock down is the timing when the golfer 7 is in the downswing when viewed from the same direction. The timing at which the golf club points in the direction of 9 o'clock is the timing at which the golf club points in the direction of 9 o'clock, and the timing at 3 o'clock is the timing in which the golf club points in the direction of 3 o'clock during the follow swing after the impact, as viewed from the same direction. In this embodiment, as measurement data by the measuring device 2, at least time-series image data from the address to the finish is captured. The photography by the cameras 21, 21, .

Although not shown, the measurement device 2 receives the image data captured by the cameras 21, 21, . . . A communication device for transmitting to the analysis device 1 is also mounted. The communication device can be of a wireless type so as not to interfere with the swing motion, or can be connected to the swing analysis device 1 in a wired manner via a cable. In this embodiment, the image data captured by the cameras 21, 21, . . . are transmitted to the swing analysis device 1 in real time via the communication device. However, for example, the image data is stored in a storage device in the cameras 21, 21, . good too.

<1-2-2. Swing analysis device>
The swing analysis device 1 is a general-purpose computer as hardware, and is implemented as, for example, a desktop computer, a notebook computer, a tablet computer, or a smart phone. As shown in FIG. 1, the swing analysis device 1 can be obtained by installing a swing analysis program 6 in a general-purpose computer from a computer-readable recording medium 30 such as a CD-ROM or via a communication line such as the Internet. manufactured. The swing analysis program 6 is software for analyzing a golf swing based on the measurement data sent from the measuring device 2, and causes the swing analysis device 1 to execute operations described later.

The swing analysis device 1 includes a display section 11 , an input section 12 , a storage section 13 , a control section 14 and a communication section 15 . These units 11 to 15 are connected to each other via a bus line 16 and can communicate with each other. The display unit 11 can be configured with a liquid crystal display or the like, and displays the golf swing analysis results and the like to the user. The input unit 12 can be composed of a mouse, a keyboard, a touch panel, or the like, and receives an operation of the swing analysis device 1 from the user.

The storage unit 13 can be configured with a hard disk or the like. The storage unit 13 stores the swing analysis program 6 as well as the measurement data sent from the measuring device 2 . The control unit 14 can be composed of a CPU, a ROM, a RAM, and the like. By reading and executing the swing analysis program 6 in the storage unit 13, the control unit 14 virtually operates as a data acquisition unit 14a, a mode development unit 14b, and a screen creation unit 14c. Details of the operation of each unit 14a to 14c will be described later. The communication unit 15 functions as a communication interface that transmits and receives data to and from an external device such as the measuring instrument 2 .

<1-3. Swing analysis method>
A swing analysis method by the swing analysis system 100 will be described below. In this method, the golf swing by the golfer 7 is measured, singular value decomposed, and decomposed into various characteristic behaviors. The method is used to understand golf swing characteristics in situations such as golf lessons, golf club fitting to golfers, and golf club development. A detailed description will be given below.

FIG. 3 is a flowchart showing the flow of the swing analysis method according to this embodiment. As shown in the figure, in the first step S1, a golf club is prepared and the golf player 7 swings the golf club. At this time, measurement is performed by the measuring device 2, and measurement data representing how the golfer 7 swings the golf club is collected. The measurement data according to the present embodiment is, as described above, data obtained by measuring the behavior of I ₀ (I ₀ =53) observation points in time series when the golfer 7 swings the golf club. The measurement data according to the present embodiment is time-series image data captured by the cameras 21, 21, . . . at least during the period from address to finish. Note that the measurement data here includes time-series image data of a plurality of systems corresponding to the imaging directions of the plurality of cameras 21, 21, . . . Measurement data measured by the measuring device 2 is transmitted from the communication device to the swing analysis device 1 . On the swing analysis device 1 side, the data acquisition unit 14 a acquires this measurement data via the communication unit 15 and stores it in the storage unit 13 .

In subsequent steps S2 to S4, the data acquisition unit 14a acquires time-series behavior data representing the behavior of the golfer 7 when he or she swings the golf club, based on the measurement data from the measuring device 2. FIG. First, in step S2, the data acquisition unit 14a acquires I ₀ observation points (I ₀ =53 in this embodiment), which is I ₁ less than I ₀ (I ₀ >I in this embodiment). ₁ ≥ 2, and particularly divided into groups of I ₁ =25). In this embodiment, the grouping method is set in advance, and observation points that are physically close to each other are grouped into the same group. In this embodiment, the same observation point is not divided into multiple groups. Also, the group here includes at least one multi-element group having a plurality of observation points as elements. In this embodiment, the I ₁ groups are all multi-element groups and contain two or more multi-element groups.

In subsequent step S3, the data acquisition unit 14a performs image processing on the image data included in the measurement data to detect images of the markers 20, 20, . Images of the markers 20, 20, . . . are detected from a plurality of photographing directions, and their positions are specified as three-dimensional coordinates. The _three -dimensional coordinates of the markers 20, 20, . is derived for

In other words, in step S3, for n=1, 2, . . . , N (N is an integer equal to or greater than 2) and i= ₁ , ₂ , . , the three-dimensional coordinates r _i (n) of the i-th observation point at the n-th time are derived. The first time is the address and the Nth time is the finish.

x _i (n), y _i (n) and z _i (n) in the above equations are the X, Y and Z direction components of r _i (n) respectively. The X, Y and Z directions are defined as shown in FIG. That is, the X direction is the direction from the back to the abdomen of the golfer 7, the Y direction is the direction of the line of flight, and the Z axis is the direction from the bottom to the top. r _i (n) is the position vector of the i-th observation point at the n-th time.

Now define the following matrix [r _i ] for the i-th observation point. The matrix [r _i ] is a matrix of N rows and 3 columns, and the three-dimensional coordinates r _i (1), r _i (2 ), . . . , r _i (N). In step S3, data [r _i ] representing the three-dimensional position in time series is derived for each of the I ₀ observation points.

In subsequent step S4, the data acquisition unit 14a derives observation point data for each group included in I ₁ groups (I ₁ =25). The observation point data for the i-th group is data representing the behavior of the i-th representative point, which is a representative point representing a plurality of observation points belonging to the i-th group (i = 1, 2, · . . , I ₁ ). That is, in step S4, for i=1, 2, . . . , I ₁ and n=1, 2, . s _i (n) representing the behavior of the representative point is derived. In this embodiment, s _i (n) is a 1-by-3 matrix representing the three-dimensional coordinates of the i-th representative point at the n-th time. The behavior (three-dimensional coordinates) of the i-th representative point at the n-th time is derived by averaging the behaviors (three-dimensional coordinates) of the plurality of observation points represented by the i-th representative point at the n-th time. In this embodiment, the behavior of representative points is calculated by simple averaging. However, without being limited to this, the behavior of the representative points may be calculated by geometric mean, weighted mean, or the like.

Observation point data for the i-th group is represented by the following matrix [s _i ]. The matrix [s _i ] is a matrix with N rows and 3 columns, and the three-dimensional coordinates s _i (1), s _i (2 ), . . . , s _i (N) are arranged. In step S4, data [s _i ] representing the three-dimensional position in time series is derived for each of the I ₁ representative points.

_Furthermore , a matrix in which I ₁ (I ₁ =25) matrices [s ₁ ], [s ₂ ], . Define [R]. The matrix [R] is a matrix of N rows and 75 (=3×25) columns.

The matrix [R] is time-series behavior data representing the behavior (position) of 25 representative points from the first time to the N-th time in time series. The matrix [R] contains observation point data [s ₁ ], [s ₂ ], . . . , [s ₂₅ ] for I ₁ groups. At step S4, a matrix [R], which is such time-series behavior data, is derived. Note that the n-th row of [R] includes three-dimensional coordinates of 25 representative points on the body of the golfer 7 at the n-th time. It shows 7 poses.

In subsequent steps S5 and S6, singular value decomposition is performed on the time-series behavior data [R] of step S4 to decompose the behavior of the golf swing represented by the time-series behavior data [R] into characteristic behaviors. More precisely, pseudo-extended data [R _a ] is created by pseudo-extending the time-series behavior data [R], and is subjected to singular value decomposition. A golf swing is an aperiodic exercise. Therefore, in the present embodiment, the golf swing is regarded as a pseudo-periodic motion and analyzed by singular value decomposition of the pseudo-extended data [R _a ] obtained by duplicating and synthesizing the golf swing.

In step S5, the data acquisition unit 14a creates pseudo extended data [R _a ] based on the time-series behavior data [R] so that the time average approaches the reference behavior. Pseudo-extended data [R _a ] are created to bring the singular value decomposition reference point closer to the reference behavior. In this embodiment, the standard behavior is the behavior at the time of address. FIG. 4(A) is a stick line formed by connecting the time averages of the positions of 25 representative points included in the time-series behavior data [R] when an actual golfer makes a golf swing. FIG. 4B is a stick diagram obtained by connecting the time averages of the positions of 25 representative points included in the pseudo extended data [R _a ] based on the same golf swing. As can be seen from the figure, the former time average is not in an address posture, but in a posture in which the arm is slightly taken back. Therefore, if the time-series behavior data [R] is subjected to singular value decomposition as it is, there is a possibility that the meaning of each mode including the first mode cannot be understood based on the address. Therefore, in the present embodiment, pseudo extension data [R _a ] is created.

More specifically, the data acquisition unit 14a creates the following additional data [R(1)] and [R _t ] based on the time-series behavior data [R]. Now, a 2N-row, 3-column matrix [ _{s i} (1 )]. Then [R(1)] replaces the 25 matrices [s ₁ (1)], [s ₂ (1)], ..., [s ₂₅ (1)] for all representative points with this It is derived as a matrix of 2N rows and 75 (=3×25) columns arranged in order in the column direction (horizontal direction).

On the other hand, the additional data [R _t ] is derived according to the following formula. That is, the additional data [R _t ] is a matrix obtained by inverting the time-series behavior data [R] in the time-series direction.

Subsequently, the data acquisition unit 14a creates pseudo extended data [R a ] by combining additional data [R(1)] and [R _t ] with the time-series behavior data [ _R ] according to the following formula. .

FIG. 5 is a conceptual diagram showing the relationship between the time series behavior data [R] and the pseudo extended data [R _a ] according to this embodiment. That is, the additional data [R(1)] obtained by repeatedly replicating the behavior at the time of address for the time length 2N is linked before the address time n=1 of the time-series behavior data [R]. Furthermore, additional data [R _t ] of time length N obtained by reversing the time-series behavior data [R] in the time-series direction is combined after the finish time n=N of the time-series behavior data [R], and then , add additional data [R(1)]. In this way, the additional data [R(1)] and [R _t ] are continuously combined with the time-series behavior data [R], and the thus-created pseudo-extended data [R _a ] are continuously Data whose value changes. The pseudo extended data [R _a ] is a matrix of 6N rows and 75 (=3×25) columns. The pseudo extended data [R _a ] created as described above is also time-series behavior data representing the behavior of the golfer 7 when swinging the golf club in time series.

In subsequent step S6, the mode development unit 14b performs singular value decomposition on the pseudo extended data [R _a ] representing the golf swing behavior according to the following equation. More specifically, the mode expansion unit 14b derives the initial behavior [R ₀ ] based on the pseudo extended data [R _a ]. Then, the mode expansion unit 14b performs singular value decomposition of the pseudo extended data [R _a ] with the initial behavior [R ₀ ] as a reference, and from the behavior of the golf swing represented by the pseudo extended data [R _a ], the characteristic , the behavior λ _j v _j z _j ^T is extracted. Note that j=1, 2, . . . , J (J is an integer of 75 or less).

The initial behavior [R ₀ ] in the above equation is the time average of [R _a ]. [R ₀ ] is a matrix of 6N rows and 75 (=3×25) columns in which an average matrix is created by averaging [R _a ] in the time direction (row direction), and 6N average matrices are arranged in the row direction. is. That is, the l-th column of [R ₀ ] is a value string in which 6N average values of the 6N components of the l-th column of [R _a ] are arranged in the row direction. By the way, as described above, the pseudo extension data [R _a ] is added with data representing the behavior (in this embodiment, the posture of the golfer 7) at address for a time length of 4N. Therefore, the behavior represented by the time average [R ₀ ] of the pseudo extended data [R _a ] is closer to the behavior at address than the behavior represented by the similar time average of the time series behavior data [R]. there is In the present embodiment, the average matrix is calculated by simple averaging, but the average matrix may be calculated by geometric averaging, weighted averaging, or the like. In addition, the initial behavior [R ₀ ] is not the time average of the entire [R _a ], but the average matrix obtained by averaging the matrix of the period before and after the address included in [R _a ] in the time direction (row direction). 6N average matrices may be arranged in the row direction. Also, the initial behavior [R ₀ ] may be obtained by arranging 6N rows corresponding to the times of the addresses included in [R _a ] in the row direction.

As described above, in the present embodiment, [R _a ]−[R ₀ ], which is the difference between the pseudo-extended data [R _a ] and its time average [R ₀ ], is singular value decomposed, and j=1, 2, . . , J (J is an integer less than or equal to 75), λ _j , z _j and v _j are derived. That is, the pseudo-extended data [R _a ] is subjected to singular value decomposition with reference to its time average [R ₀ ]. λ _j is the singular value of the j-th mode and represents the ratio of the j-th mode to [R _a ]-[R ₀ ]. v _j is the left singular vector of the j-th mode of [R _a ]-[R ₀ ] and is N-dimensional. z _j is the right singular vector of the j-th mode of [R _a ]-[R ₀ ] and has 75 dimensions. z _j is the basis representing the excitation pattern of the behavior of each representative point on the body of the golfer 7 in the j-th mode, and v _j is the basis representing the excitation pattern of z _j with respect to time in the j-th mode.

Further, the mode expansion unit 14b, for _j =1 _, 2, _. derived according to

By the above singular value decomposition, from the pseudo extended data [R _a ] that represents the behavior of the golf swing in time series as well as the time series behavior data [R], each mode from the first mode to the J mode included in the golf swing The corresponding characteristic behavior λ _j v _j z _j ^T is extracted. Using this result, the mode expansion unit 14b converts the characteristic behavior λ _j v _j z _j ^T of the j-th mode to the initial behavior [R ₀ ] to derive the behavior of the j-th mode [R _j ]. Since [R _j ] is based on the characteristic behavior λ _j v _j z _j ^T of the j-th mode decomposed from the behavior of the golf swing, hereinafter, the behavior represented by [R _j ] may be referred to as decomposition behavior. .

Note that J is 75 at maximum, but up to what mode the behavior is to be derived can be appropriately selected according to the purpose of the analysis and the like. According to the studies of the present inventors, generally, the contribution rate of the first mode alone is about 90%, and the cumulative contribution rate from the first mode to the second mode is about 97%. The cumulative contribution rate up to the third mode exceeds 99%, and the cumulative contribution rate from the first mode to the fifth mode reaches about 99.8%. Therefore, by deriving the behavior up to the fifth mode, the golf swing can be roughly evaluated.

In addition, the mode expansion unit 14b expresses a behavior obtained by accumulating behaviors from the first mode to the k-th mode for k=1, 2, . . . ₁ ~ _k ] are derived according to the following formula. [R ₁ ~ _k ] is based on the characteristic behavior λ _j v _j z _j ^T from the first mode to the k-th mode decomposed from the behavior of the golf swing, so hereinafter, the expression of [R ₁ ~ _k ] Behavior may also be referred to as decomposition behavior.

[R ₁ to _k ] includes cumulative behaviors (three-dimensional coordinates) from the first mode to the k-th mode at each time of each representative point as components. Therefore, deriving [R ₁ to _k ] for k=1, 2, . . . , J means deriving the golfer's posture at each time in each mode.

Steps S1 to S6 described above can be repeatedly performed for multiple golf swings performed by the same or different golf players using the same or different golf clubs.

In subsequent step S7, the screen creating unit 14c creates a screen for displaying the result of singular value decomposition (hereinafter referred to as a result screen) and causes the display unit 11 to display it. For example, the result screen can display a stick diagram as shown in FIG. FIG. 6 shows the calculation of [R ₁ ] (=[R ₁ ~ ₁ ]) representing the behavior of the first mode when a certain golfer makes a golf swing, and the three-dimensional representation of 25 representative points included in this. It is a stick diagram formed by connecting coordinates. The figure shows stick diagrams at seven times from address to finish. Instead of or in addition to [R ₁ ], [R ₁ ~ _k ] is also calculated for k≧2, and stick diagrams at various times in the k-th mode based on this are displayed on the result screen. You may A user viewing such a stick diagram can appropriately evaluate individual behaviors included in the golf swing and understand the characteristics of the golf swing.

The result screen can also display a comparison of stick diagrams when the same or different golfers swing the same or different golf clubs. A comparative diagram is, for example, a diagram in which a plurality of stick diagrams are displayed overlaid or side by side. At this time, stick diagrams for different golf swings derived by repeating steps S1 to S6 are typically assumed as the plurality of stick diagrams to be compared. However, the behavior [R _1-k ] previously stored in the storage unit 13 or externally acquired via the communication unit 15 is used as a comparison target for the stick diagrams derived in steps S1 to S6. Based stick diagram may be selected. For example, a stick diagram based on the behavior [R _1-k ] of an ideal golf swing of an advanced golfer may be compared.

As an example, FIG. 7 is an overlay of stick diagrams of various modes at the timing of impact when the same golfer performs a draw swing and a fade swing with the same golf club. To give another example, FIG. 8 is a diagram in which stick diagrams of various modes at the timing of impact are superimposed when different golfers G1 and G2 swing using their respective golf clubs. . A user viewing such a diagram can compare different golf swings at the level of individual behaviors involved in the golf swings, and can properly understand the differences in characteristics between the golf swings.

As shown in Non-Patent Documents 1 and 2, it is known that the behaviors of the first to fifth modes are as follows. Together with such knowledge, it is also possible to deepen the understanding of golf swing characteristics that appear in stick diagrams.

The result screen can also display the singular value λ _j and the contribution C _j for j=1, 2, . . . , J. Also, for k=1, 2, . . . , J, the cumulative contribution rate C ₁ +C _{2 +} .

Further, the mode expansion unit 14b not only reproduces the behavior of each mode as a diagram like a stick diagram, but also j=1, 2, . , the modal behavior [R _j ], [R _j ]-[R ₀ ], [R ₁ - _k ] and [R ₁ - _k ]-[R ₀ ] can be variously analyzed. For example, considering that the second mode represents the rotation of the shoulder in the entire swing (see Table 1), the mode expansion section _14b performs [R ₂ ], [R ₂ ]-[R ₀ ], [R _1-2 ] and [R _1-2 ]-[R ₀ ], the amount of shoulder rotation can be evaluated qualitatively or quantitatively _. Further, the mode expansion unit 14b may detect a portion of the golf swings to be compared where there is a significant difference in behavior. The screen creating unit 14c can also display the result of such further analysis on the result screen.

In the subsequent step S8, the mode development unit 14b corrects the right singular vector _zj for a certain golf swing derived in steps S1 to S6, and estimates new behavior of the golfer 7. FIG. In this embodiment, step S8 is performed when the user desires, and is performed in detail as shown in FIG.

First, as sub-steps S11 and S12 of step S8, the mode expansion unit 14b performs the right behavior λ _j v _j z _j ^T corresponding to at least one mode j among the first to J-th modes. Modify the singular vectors z _j . Hereinafter, the mode corresponding to the right singular vector z _j to be corrected may be referred to as the attention mode. Here, the right singular vector z _j is the basis representing the excitation pattern of the behavior of each representative point on the body of the golfer 7 in the j-th mode, as described above.

FIG. 10 shows values of 75 components contained in the fourth mode right singular vector z ₄ corresponding to the example of FIG. As is clear from the above description, the 75 components included in the right singular vector z _j represent the magnitudes of the excitation of the behavior (position) of the 25 representative points in the X, Y, and Z directions, respectively. In FIG. 10, 75 components are arranged along the horizontal axis, and the vertical axis indicates the value (magnitude of excitation) of each component. On the other hand, FIG. 11 shows values of many components contained in the left singular vector v ₄ of the fourth mode corresponding to the example of FIG. As already mentioned, the left singular vector v _j is the basis for the excitation pattern over time for z _j in the j mode. In FIG. 11, the horizontal axis indicates the time axis, and the vertical axis indicates the value of the component (magnitude of excitation) at each time.

In sub-step S11, the mode expansion unit 14b determines one or a plurality of attention modes to be modified among the first to Jth modes according to the input from the user. In addition, the mode expansion unit 14b corrects one or _more components (hereinafter sometimes referred to as a target component ) and the amount of correction for each component of interest.

When the user sets the attention mode, the attention component, and the correction amount thereof, the user can refer to the result screen in step S7. For example, consider a case where the user attempts to correct the posture of the draw swing at the time of impact so as to bring it closer to the posture of the fade swing. In this case, referring to the stick diagram at the time of impact in FIG. 7, the difference between the two golf swings becomes remarkable from the fourth mode, and the difference is particularly seen in the movement of the right elbow. Therefore, from the stick diagram in FIG. 7 (especially refer to the dotted box), the fourth mode can be selected as the mode of interest, and the three components corresponding to the behavior (three-dimensional position) of the right elbow can be selected as the components of interest. . Also, while referring to the stick diagram in FIG. 7, the user sets arbitrary correction amounts for the values of the three components corresponding to the behavior of the right elbow in the X, Y, and Z directions in FIG. . In order to assist the user in setting the amount of correction, the result screen displays the right singular vector z _j and the left singular vector v A graph of the components of _j may be displayed. At this time, the user reads the magnitude of the current impact excitation from the graph of the left singular vector v _j in FIG. 11, and from the stick diagram in FIG. Further, from the graph of the right singular vector z _j in FIG. 10, the value of the component of interest in the fourth mode can be read, and the amount of correction can be determined by integrating these values. For setting the amount of correction, a correction magnification such as 1.1 times or 0.98 times may be input.

When the user sets the attention mode, the attention component, and the amount of correction thereof via the input unit 12, the mode expansion unit 14b corrects the right singular vector z _j of the attention mode based on these information (substep S12). More specifically, the mode expansion unit 14b corrects the value of each target component included in the right singular vector _zj of each target mode according to each correction amount. Below, the corrected right singular vector z _j of the component of interest is represented as z _j ′.

In subsequent sub-step S13, the mode expansion unit 14b reconstructs the characteristic behavior λ _j v _j z _j ^T corresponding to the mode of interest based on the corrected right singular vector z _j ', and reconstructs the characteristic behavior Derive λ _j v _j z _j ' ^T. In addition, the mode expansion unit 14b expands the decomposition behaviors [R _j ] and [R ₁ to _k ] based on the modified characteristic behaviors λ _j v _j z _j ' ^T for each mode after the mode of interest. Reconfigure. 10 and 11, by replacing λ _j v _{j z j} ^T of the mode of interest with λ _j v _j z _j ′ ^T , the decomposition behaviors [R _j ]′ and [R ₁ ~ _k ]' is derived.

The behaviors [R _j ]' and [R _{1 -k} ]' from the attention mode to the J-th mode are new behaviors obtained by modifying the original behaviors [R _j ] and [R _{1 -k} ]. FIG. 12 shows the behavior (position) of the right elbow in the X, Y, and Z directions in the fourth mode so that the draw _swing in FIG. ₇ is closer to the fade swing. is a stick diagram at the time of impact based on. In addition, in FIG. 12, the behavior (position) of the part such as the right hand on the tip side of the right elbow is translated along with the correction of the right elbow. In this manner, the behavior of the unrestrained portion on the distal side of the portion to be corrected may be corrected in the same manner as the portion to be corrected so that the actual change in behavior can be easily visualized. FIG. 13 is a diagram obtained by correcting the stick diagram at the time of impact based on [R ₁ to ₈ ]' of a beginner, who was pointed out that the upper body moved too far forward, by the method of steps S11 to S13. is. In the example of FIG. 13, the component of interest corresponding to the upper body included in the right singular vector z _j of the eighth mode is corrected so that the upper body moves backward. In FIG. 13 as well, as in FIG. 12, the behavior of the unconstrained parts such as the head, right arm, left arm, etc. on the tip side of the upper body is translated along with the correction of the behavior of the upper body.

The screen creating unit 14c displays the analysis result of step S8 on the result screen. The analysis results of step S8 here include stick diagrams as shown in FIGS. 12 and 13 show comparison diagrams of behavior after modification, behavior before modification and/or target behavior for modification, but they are not comparison diagrams, only behavior after modification. A stick diagram shown may be displayed. Further, the mode expansion unit 14b not only reproduces the modified behavior as a diagram such as a stick diagram, but also j=1, 2, . , similar to the analysis of behavior before modification, behavior after modification [R _j ]′, [R _j ]′−[R ₀ ], [R ₁ ~ _k ]′ and [R ₁ ~ _k ]′-[R ₀ ] can be analyzed in various ways. The screen creating unit 14c can also display the result of such further analysis on the result screen.

<2. Second Embodiment>
Next, a second embodiment of the invention will be described. 2nd Embodiment differs only in the content of step S8 of the swing analysis method shown in FIG. 3 compared with 1st Embodiment. Therefore, only the content of step 8 according to the second embodiment will be described below. Also in step S8 according to the second embodiment, the mode development unit 14b corrects the right singular vector z _j for a certain golf swing derived in steps S1 to S6, and estimates new behavior of the golfer 7. FIG.

Step S8 according to the second embodiment is executed as shown in FIG. First, as sub-steps S21 to S23 of step S8, the mode expansion unit 14b performs the right behavior λ _j v _j z _j ^T corresponding to at least one mode j among the first to J-th modes. Modify the singular vectors z _j . Also in the second embodiment, the mode corresponding to the right singular vector z _j to be corrected may be called the attention mode. In the second embodiment, a golf swing is modified to be closer to another golf swing (hereinafter referred to as a target swing _{) .} is modified to approach

In sub-step S21, the mode expansion unit 14b determines one or a plurality of attention modes to be modified among the first to Jth modes according to the input from the user. Further, the mode development unit 14b determines the target base w _j for each attention mode according to the input from the user. The method by which the user sets the attention mode is the same as in the first embodiment. On the other hand, the user designates a target swing for setting the target basis w _j . The mode expansion unit 14b acquires the right singular vector _zj of the attention mode that constitutes the behavior of the target swing specified by the user, and determines it as the target basis _wj . Note that the target basis w _j may be obtained by repeating steps S1 to S6, may be stored in the storage unit 13 in advance, or may be obtained from the outside via the communication unit 15. FIG. A target swing can be, for example, an ideal golf swing for an advanced player.

In the _second embodiment, the right singular vector z _j of the mode of interest is modified so as to approach the target basis w _j . The right singular vector z _j of (hereinafter referred to as pair mode) is also modified. This _is to ensure orthogonality among the right singular vectors z ₁ , z ₂ , _. That is, in the first embodiment, the correction of the right singular vector z _j of the mode of interest may impair the orthogonality between the right singular vector z _j of the mode of interest and the right singular vectors z _j of other modes. is high (see FIG. 15A). A golf swing can be modeled even if the orthogonality is lost, but if the orthogonality is lost to a large extent, the model may become unsuitable. The correction algorithm of the second embodiment can solve this problem.

In subsequent sub-step S22, the mode development unit 14b selects a pair mode to be paired with each attention mode from among the first to Jth modes. In the present embodiment, among the first to Jth modes, all modes other than the attention mode (hereinafter referred to as candidate modes) are candidates for the pair mode. The mode development unit 14b sequentially performs provisional pairing with the attention mode for all candidate modes. Then, for each tentative pairing, the right singular vector z _j of the mode of interest is rotated around the axis corresponding to the tentative pairing so as to approach the target basis w _j (see FIG. 15B). The axis corresponding to the tentative pairing is the axis orthogonal to both the right singular vector z _j of the mode of interest and the right singular vector z _j of the candidate mode with which it is tentatively paired.

At this time, in this embodiment, the right singular vector z _j of the mode of interest is rotated so as to be closest to the target basis w _j . The distance d between the right singular vector z _j of the mode of interest and the target basis w _j can be expressed by the residual sum of squares (z _j −w _j ) ² of both vectors. Note that since z _j ² = w _j ² = 1, the residual sum of squares (z _j - w _j ) ² = z _j ² + w _j 2 ^- 2 z _j · w _j = 2 - 2z _j · w _j . On the other hand, the correlation coefficient c between the right singular vector z _j of the mode of interest and the target basis w _j is expressed by the following equation, and its denominator is 1 because it is the norm of the mode. Therefore, when the right singular vector z _j of the attention mode is closest to the target basis w _j , it is determined that the distance d is the smallest, that is, the correlation coefficient c is the largest.

The mode expansion unit 14b rotates the right singular vector _zj of the mode of interest in small increments within a certain range, and calculates the correlation coefficient c between the right singular vector _zj of the mode of interest after rotation and the target basis _wj . Then, the rotation angle θ at which the correlation coefficient c is maximized and the maximum correlation coefficient c _max are specified. At this time, for example, it can be rotated in steps of π/1000 within the range of -π/2 to π/2. Note that the distance d=(z _j −w _j ) ² is an error function representing the error between the right singular vector z _j of the mode of interest after rotation and the target basis w _j . A rotation angle θ to be minimized is derived. Then, after deriving the correlation coefficient c _max for each candidate vector as described above, the candidate mode that provides the rotation that maximizes the correlation coefficient c _max corresponding to each of the candidate vectors is paired. Select as mode.

In subsequent sub-step S23, the mode developing unit 14b rotates the right singular vector z _j of the mode of interest together with the right singular vector z _j of the pair mode around an axis orthogonal to both of these vectors (see FIG. 15B). The rotation angle at this time is the rotation angle θ at which the maximum correlation coefficient c _max is given to the right singular vector z _j of the attention mode (that is, the error function is minimized), and has already been specified in sub-step S22. there is As described above, the right singular vector z _j of the attention mode and the right singular vector z _j of the pair mode are corrected by being rotated in the same direction by the same amount. Also in the second embodiment, the corrected right singular vector z _j is represented as z _j ′. After such rotation, the right singular vector z _j ' of the mode of interest and the right singular vector z _j ' of the pair mode maintain orthogonality with the right singular vectors z _j of the remaining modes.

After sub-step S23, sub-step S13 similar to that of the first embodiment is executed. FIG. 16 is a stick diagram based on [R _{1 -8} ]' when correcting the right singular vector z _j through substeps S21-S23 so as to bring a certain golf swing closer to the target swing. In this example, the first and third modes were selected as attention modes, and the second and fourth modes were selected as their respective pair modes. As shown in the figure, according to the second embodiment, the original golf swing can be brought closer to the target swing.

<3. Third Embodiment>
Next, a third embodiment of the invention will be described. The third embodiment differs from the first and second embodiments only in the content of step S8 of the swing analysis method shown in FIG. Therefore, only the content of step S8 according to the third embodiment will be described below. Also in step S8 according to the third embodiment, the mode development unit 14b corrects the right singular vector z _j for a certain golf swing derived in steps S1 to S6, and estimates new behavior of the golfer 7. FIG.

Step S8 according to the third embodiment is executed as shown in FIG. First, as sub-steps S31 to S34 of step S8, the mode expansion unit 14b performs the right behavior λ _j v _j z _j ^T corresponding to at least one mode j among the first to J-th modes. Modify the singular vectors z _j . Also in the third embodiment, the mode corresponding to the right singular vector z _j to be corrected may be called the attention mode.

In sub-step S31, the mode development unit 14b determines one or a plurality of attention modes to be modified among the first to J-th modes according to an input from the user. The method by which the user sets the attention mode is the same as in the first and second embodiments. Further, the mode development unit 14b determines the target base w _j for each attention mode according to the input from the user. The method by which the user sets the target basis w _j is the same as in the second embodiment, and designates the target swing.

In the third embodiment, as in the second embodiment, the right singular vector z _j of the attention mode is corrected so as to approach the target base w _j that constitutes the behavior of the target swing, and is paired with the attention mode. The pair mode right singular vector z _j is also modified. This _is to ensure orthogonality among the right singular vectors z ₁ , z ₂ , _. Hereinafter, for distinction, the right singular vector _zj of the mode of interest to be corrected may be called _ztj , and the right singular vector _zj of the pair mode to be corrected may be called _zpj . In the third embodiment, not only is the right singular vector _ztj of the mode of interest corrected to approach the target basis _wj , but also the right singular vector _zpj of the pair mode approaches a predetermined target basis _wpj . modified as follows:

In subsequent sub-step S32, the mode development unit 14b selects a pair mode to be paired with each attention mode from among the first to Jth modes. Also, the mode expansion unit 14b determines a target base w _pj for each pair mode. In this embodiment, the pair mode is selected according to which mode is the attention mode according to a predetermined rule. For example, if the attention mode is the first mode, the second mode is the pair mode, if the attention mode is the second mode, the first mode is the pair mode, and if the attention mode is the third mode, the fourth mode is the A rule is predetermined such that the mode is the pair mode. Further, the mode development unit 14b acquires the right singular vector _zj of the pair mode that constitutes the behavior of the target swing specified by the user in step S31, and determines this as the target basis _wpj .

In subsequent sub-step S33, the mode expansion unit 14b calculates a rotation angle _θr for rotating the right singular vector _ztj of the mode of interest and the right singular vector _zpj of the pair mode. θ _r can be calculated as follows.

First, consider rotating the right singular vector z _tj of the mode of interest and the right singular vector z _pj of the pair mode by an angle θ around the axis orthogonal to these vectors z _tj and z _pj . At this time, this rotation can be expressed as follows. Note that z _tj ' and z _pj ' are the rotated right singular vectors z _tj and z _pj , respectively.

Also, an error function E is defined as follows. The first term represents the error between the right singular vector z _tj ' of the mode of interest after rotation and the target base w _j which is the target value to bring it close to. The second term represents the error between the right singular vector z _pj ' of the pair mode after rotation and the target basis w _pj which is the target value for bringing this closer.

The above formula is expanded as follows. Note that [I] is a unit matrix.

Furthermore, substituting the formula of formula 13 into the formula of formula 15 yields the following formula. The error function E is a function of θ.

Bringing the right singular vectors z _tj and z _pj closer to their respective target bases w _j and w _pj is to minimize the error function E. Also, when the error function E is minimized, the error function E takes an extremum. Therefore, as shown in the following formula, the error function E of Equation 16 is differentiated, and θ at which this becomes zero is calculated.

The above equation is transformed into the following equation. The mode expansion unit 14b calculates θ that minimizes the error function E according to the following formula, and sets this as the rotation angle _θr .

In the following step S34, the mode expansion unit 14b converts the right singular vector _{ztj of} the mode of _interest , together with the right singular vector _zpj of the pair mode, to a rotation angle θ _r only rotate. As described above, the right singular vector z _tj of the attention mode and the right singular vector z _pj of the pair mode are rotated in the same direction by the same amount and corrected.

In subsequent step S35, similar to step S13 described above, the mode expansion unit 14b generates characteristic behavior λ _j v _j z _tj ' ^T corresponding to the mode of interest based on the corrected right singular vector z _tj '. Reconfigure. Also, the mode expansion unit 14b reconstructs the characteristic behavior λ _j v _j z _pj ' ^T corresponding to the pair mode based on the corrected right singular vector z _pj '. Furthermore, in the same manner as in step S13 described above, the mode expansion unit 14b, based on the modified characteristic behaviors λ _j v _j z _tj ' ^T and λ _j v _j z _pj ' ^T , decomposes behavior [R _j ] and Reconstruct [R _{1 -k} ]. At this time, in the formulas 10 and 11, by replacing λ _j v _{j z j} ^T of the attention mode and the pair mode with λ _j v _j z _tj ' ^T and λ _j v _j z _pj ' ^T , respectively, , the modified decomposition behaviors [R _j ]′ and [R _{1˜k ]} ′ are derived. The analysis result of step S8 is appropriately displayed on the result screen as in the first and second embodiments.

<4. Features>
<4-1>
According to step S8 of the first to third embodiments, it is possible to correct only the behavior of some modes included in the original measured behavior. Thus, the new behavior after modification retains the properties of the original behavior. For example, beginners often do not know how to correct their actions if they are shown an ideal golf swing but the difference from their own golf swing is too great. However, if you are shown an example of operation that leaves your own personality, it is easy to imagine how to correct it. Postures reconstructed from [R _{1 -k} ]' for higher k, eg, k=10, can give golfers useful guidance for improving their golf swing. The correction in step S8 as described above enables simulation of a new golf swing. In addition, the behavior after correction can bring about various findings in golf lesson situations, golf club fitting situations, golf club development situations, and the like.

<4-2>
According to the above embodiment, the number of modes (number of dimensions) in subsequent singular value decomposition is reduced by combining I ₀ observation points into a smaller number of I ₁ representative points. That is, if the number of points of interest (observation points or representative points) to be subjected to singular value decomposition is large, the degree of freedom of the swing will be high, but the number of modes will increase accordingly, and the information possessed by one mode will be small. Become. In this case, it may rather be difficult to appropriately evaluate individual behaviors included in the golf swing from the results of singular value decomposition. On the other hand, if the number of observation points is blindly reduced in order to reduce the number of modes, the accuracy of swing analysis may decrease. In this regard, in the above embodiments, a plurality of observation points are grouped and information on the plurality of observation points is compressed into information on one representative point. Therefore, the amount of information in each mode can be maintained while maintaining the accuracy of swing analysis. Therefore, individual behaviors (behaviors in each mode) included in the golf swing can be evaluated more appropriately.

FIG. 6, already described, is a first mode stick diagram of 25 representative points. On the other hand, FIG. 17 is a stick diagram obtained by connecting three-dimensional coordinates of 53 observation points in the first mode based on the same measurement data as in FIG. 6 without creating representative points. As can be seen by comparing FIG. 6 and FIG. 17, even if the points of interest are reduced, the entire swing behavior is successfully expressed. On the other hand, the expansion and contraction of the upper body can be seen from the stick diagram of FIG. 17, which has many points of interest. In contrast, the stick diagram of FIG. 6, which has fewer points of interest and is simpler, shows rotational movement rather than extension and contraction of the upper body. In this way, new information can be obtained by compressing the points of interest and expressing the behavior more simply.

In addition, when the behavior is expressed simply by reducing the number of modes as described above, it becomes easier to compare different swings. In other words, if there are too many points of interest to be subjected to singular value decomposition, the physique, posture, etc. of the golfer will be reproduced too accurately, making comparison rather difficult. In such a case, the problem can be solved by representing the swing with a simple behavior.

Further, by averaging the behavior of a plurality of observation points to the behavior of one representative point, it is possible to cut the rotation information. For example, rotation of the hips about the direction of the line of flight may be less needed in analyzing a golf swing. In such a case, by combining the observation points near the waist into one representative point, it is possible to reduce unnecessary information and focus on more necessary information.

<5. Variation>
Although several embodiments of the present invention have been described above, the present invention is not limited to the above embodiments, and various modifications are possible without departing from the gist of the present invention. For example, the following changes are possible. Also, the gist of the following modified examples can be combined as appropriate.

<5-1>
The configuration of the measuring device 2 described above is an example. For example, the measuring device 2 may be an inertial sensor, a distance image sensor, or the like, or may be selected from the group consisting of an inertial sensor, a distance image sensor, and a motion capture system. Any combination of two or more devices may be used.

<5-2>
In the above embodiment, the golf swing was analyzed, but the analysis can also be performed on swings of hitting tools other than golf clubs, such as tennis rackets and baseball bats.

<5-3>
In the above embodiment, the reference behavior is the behavior at the time of address. However, the reference behavior can also be behavior at other times, such as impact or top behavior. For example, if the behavior at the top is used as the reference behavior, pseudo-extended data can be created as shown in FIG. Pseudo extended data can be created. In this case, the initial behavior [R ₀ ] approaches the behavior at impact or top.

<5-4>
In the above embodiment, the observation point data to be subjected to singular value decomposition is data representing the position of the representative points in time series. , or a combination of data representing two or more elements selected from the group consisting of these and positions in time series. Note that the orientation here is a parameter having angle information such as a quaternion.

<5-5>
In the above embodiment, the observation point was set only on the golfer's body, but the observation point may be set on the golf club.

<5-6>
The I ₁ groups that divide the I ₀ observation points may include a single element group whose element is one observation point. In this case, the observation point data corresponding to the single element group can be data representing the behavior of one observation point belonging to the single element group in chronological order.

<5-7>
In the above embodiment, the observation points are grouped so that the same observation points are not redundantly divided into a plurality of groups. However, it is also possible to divide one or more observation points into multiple groups redundantly.

<5-8>
In the above embodiment, the process of dividing I ₀ observation points into I ₁ groups, which are less than I ₀ , may be omitted. In this case, in step S4, _a matrix obtained by arranging I ₀ matrices [r ₁ ], [r ₂ ], . If the time-series behavior data [R] is derived, subsequent processing can be executed in the same manner as in the above embodiment.

<5-9>
In the above embodiment, the pseudo-extended data [R _a ] is subjected to singular value decomposition, but the time-series behavior data [R] may be subjected to singular value decomposition.

<5-10>
The behavior of the representative point may be derived by other methods instead of averaging the behaviors of the plurality of observation points represented by the representative point. As the behavior of the representative point, for example, the largest behavior among the behaviors of the plurality of observation points represented by the representative point may be selected, or the largest behavior and the smallest behavior may be averaged.

<5-11>
In sub-step S11 of the first embodiment, the mode of interest, the component of interest, and the correction amount are determined according to the input from the user. However, at least one of these may be automatically determined by optimization so that the corrected behavior approaches the target behavior. Similarly, in sub-step S21 of the second embodiment and sub-step S31 of the third embodiment, the attention mode was determined according to the input from the user. may be determined automatically by optimization.

<5-12>
In the second embodiment, a mode that maximizes the correlation coefficient c _max is selected as the pair mode, but the pair mode is not limited to this and can be arbitrarily selected from modes other than the attention mode.

<5-13>
In sub-step S23 of the second embodiment, when rotating the right singular vector z _j of the attention mode and the right singular vector z _j of the pair mode, it is not necessary to rotate the former so as to approach the target basis w _j . For example, it may be rotated by an arbitrary amount specified by the user. Similarly, in the third embodiment, the right singular vector z _j of the attention mode and the right singular vector z _j of the pair mode can be rotated by an arbitrary amount of rotation.

<5-14>
In step S32 of the third embodiment, the pair mode is selected according to which mode is the attention mode according to a predetermined rule. However, as in the second embodiment, among the first to Jth modes, all modes other than the attention mode may be candidate modes for the pair mode. In this case, the mode development unit 14b sequentially performs provisional pairing with the attention mode for all candidate modes. Then, the rotation angle θ _r that minimizes the error function E is calculated for each provisional pairing, and this θ _r is substituted into the equation (16) to calculate the value of the error function E. Then, among all the candidate modes, the candidate mode that gives the minimum value of the error function E may be finally determined as the pair mode.

<5-15>
The definition formula of the error function E is not limited to the one shown in Equation 14. For example, as in the following formula, only the term representing the error between the right singular vector z _tj ' of the attention mode after rotation and the target basis w _j may be configured.

In this case, θ that minimizes the error function E is calculated by the following formula.

1 Swing analysis device (computer)
100 swing analysis system 14a data acquisition unit 14b mode development unit 14c screen creation unit 2 measuring device 6 swing analysis program 7 golfer

Claims (11)

a data acquisition unit that acquires time-series behavior data representing the behavior of a plurality of points of interest when the player swings the hitting tool in time series;
A mode expansion unit that decomposes the behavior by singular value decomposition of the time series behavior data,
The mode expansion unit is
Extracting a plurality of characteristic behaviors corresponding to a plurality of modes from the behavior by singular value decomposition of the time series behavior data,
Modifying a first basis, which is a basis representing an excitation pattern of the behavior of the plurality of points of interest, constituting the characteristic behavior corresponding to at least one mode of interest among the plurality of modes,
reconstructing the characteristic behavior corresponding to the attention mode based on the modified first basis;
Swing analysis device. wherein the mode expansion unit corrects the value of at least one component among a plurality of components respectively corresponding to behaviors of the plurality of points of interest included in the first basis;
The swing analysis device according to claim 1. The mode development unit, according to an input from a user, selects at least one of the plurality of modes to be modified, at least one of the plurality of components to be modified, and at least one of the plurality of components to be modified. determining at least one of the component correction amounts;
The swing analysis device according to claim 2. The mode expansion unit is
The first basis of the mode of interest is set to the first basis of the mode of interest and the first basis of the pair mode together with the first basis of a pair mode different from the mode of interest among the plurality of modes. modify by rotating about orthogonal axes,
The swing analysis device according to claim 1. The mode expansion unit is
For each of a plurality of candidate modes other than the mode of interest among the plurality of modes, the first basis of the mode of interest is set so that the first basis of the mode of interest approaches a target value. rotate about an axis orthogonal to the first basis of the mode of interest and the first basis of the candidate modes;
Selecting, as the pair mode, the candidate mode that provides a rotation that maximizes the correlation coefficient between the first basis of the attention mode after the rotation and the target value;
The swing analysis device according to claim 4. The mode expansion unit is
calculating a rotation angle that minimizes an error function including a term representing an error between the first basis of the attention mode after rotation and its target value;
modifying the first basis of the mode of interest together with the first basis of the pair mode by rotating the rotation angle about the axis;
The swing analysis device according to claim 4. the error function further includes a term representing the error between the first basis of the paired mode after rotation and its target value;
The swing analysis device according to claim 6. The time-series behavior data is data representing at least one of positions, orientations, velocities, accelerations, angular velocities, angular accelerations, forces, and torques of the plurality of points of interest in time series.
The swing analysis device according to any one of claims 1 to 7. The hitting tool is a golf club,
The swing analysis device according to any one of claims 1 to 8. Acquiring time-series behavior data representing in time-series behavior of a plurality of points of interest when a player swings a hitting tool;
decomposing the behavior by singular value decomposition of the time series behavior data;
Decomposing the behavior includes:
Extracting a plurality of characteristic behaviors respectively corresponding to a plurality of modes from the behavior by singular value decomposition of the time-series behavior data;
Modifying a first basis representing an excitation pattern of the behavior of the plurality of points of interest, which constitutes the characteristic behavior corresponding to at least one mode of interest among the plurality of modes;
reconstructing the characteristic behavior corresponding to the attention mode based on the modified first basis;
Swing analysis method. Acquiring time-series behavior data representing in time-series behavior of a plurality of points of interest when a player swings a hitting tool;
causing a computer to decompose the behavior by singular value decomposition of the time-series behavior data;
Decomposing the behavior includes:
Extracting a plurality of characteristic behaviors respectively corresponding to a plurality of modes from the behavior by singular value decomposition of the time-series behavior data;
Modifying a first basis representing an excitation pattern of the behavior of the plurality of points of interest, which constitutes the characteristic behavior corresponding to at least one mode of interest among the plurality of modes;
reconstructing the characteristic behavior corresponding to the attention mode based on the modified first basis;
Swing analysis program.

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