JP2001021320A - Six-degree-of-freedom motion analyzing method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an analysis method analyzing the 6-degree of freedom motion of a rigid body by using image data picked up from only one direction. SOLUTION: In this analyzing method, a reference circle 10 is set in a unified body with a rigid body, a reference point 20 is formed on the circle 10, and the image of the point 20 is picked up intermittently at fine time intervals by using a fixed camera. From image data of the reference circle 10 and the reference point 20 which are obtained every moment, the center coordinate and the rotation angle of the reference circle 10 are calculated in order. Thereby 3-degree-of-freedom translation and 3-degree-of-freedom rotational motion of the rigid body are analyzed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing the motion of a rigid body in a non-contact manner based on image data taken by a camera, and more particularly to a method for analyzing a rigid body based on an image taken from only one direction. The present invention relates to a 6-DOF motion analysis method.

[0002]

2. Description of the Related Art In research and development of aircraft, rockets, automobiles, and the like, it is important to know the aerodynamic force acting on a rigid body, and until now, it has mainly been determined by experiments using a wind tunnel. To find the force, use a balance or pressure sensor [Ref.
2], and a potentiometer or the like for obtaining displacement is used, but friction or inertia caused by a lead wire from a sensor or a mechanism for detecting displacement may affect the movement. In addition, the degree of freedom of movement may be limited depending on the displacement detection method. Therefore, a motion analysis using image data, which is one of the non-contact measurement methods that do not affect the motion and the degree of freedom [see Reference 3], is a very useful means.

[0003] In an earthquake or conflict area, relief supplies are often supplied by airdrop from an aircraft. In order to supply precision equipment such as medical equipment and to drop supplies to precise locations, techniques that control the movement of the falling rigid body and make it soft landing are required. Also, from the viewpoint of attitude control when the spacecraft re-enters the atmosphere, it is important to analyze the motion of a rigid body that falls under aerodynamic forces. Until now, studies on falling rigid bodies with unsteady motion have been conducted, but the degree of freedom of motion is limited in many cases, such as in a vertical plane [see References 4 and 5].

[0004] As an analysis method using an image that does not affect the movement without contact, a method that uses image data obtained by photographing from two directions has been put to practical use. This analysis method is a method in which a plurality of reference points are set on a rigid body, and the position and rotation angle of the rigid body are calculated using disparity generated in the image from two directions. This is a close approach.

[0005]

However, in the above-mentioned conventional method, the images taken by the two cameras must be synchronized, so that the operation is complicated and difficult, and the cost is high. Another problem is that two high-speed cameras are required, and the cost of experiments and measurements increases.

The present invention has been made in order to solve such a problem, and an object of the present invention is to provide an analysis method for analyzing a six-degree-of-freedom motion of a rigid body using image data taken from only one direction. I do.

According to the analysis method of the present invention, if a difference method or a polynomial approximation method of a conventional method is applied to the analysis result of the motion (position and rotation data) of a rigid body obtained in a non-contact manner and without affecting the motion, The acceleration of the rigid body and the aerodynamic force acting on the rigid body falling in the air can be calculated.

[0008]

According to the first aspect of the present invention, a reference circle is provided integrally with a rigid body, and at least three reference points are formed on the reference circle. ,
The image of the reference point is intermittently photographed at a minute time interval using a single fixed camera, and from the image data of the reference point obtained every moment, the center position coordinates of the reference circle and the coordinates of the reference circle are obtained. A six-degree-of-freedom motion analysis method characterized by sequentially calculating a rotation angle in space and analyzing a translational motion having three degrees of freedom and a rotational motion having three degrees of freedom of the rigid body.

According to this analysis method, a six-degree-of-freedom motion analysis of a rigid body can be performed only by photographing from one direction.

According to a second aspect of the present invention, in the six-degree-of-freedom motion analysis method according to the first aspect, the image data and
With reference to the symbols defined in the table below, said at least 3
Three reference points are selected from the three reference points to form one set, and one set 3
The (x, z) coordinates of the reference points and φ, which is the angle between the major axis of the ellipse formed by inclining the reference circle and the x-axis, are obtained, and these values are sequentially calculated by the following equation (7). substituted to (12), further, the radius r of the reference circle is calculated to obtain the y ₀ and a pre-calibrated shrinkage R, 6 pieces of the center coordinate is a spatial parameter of the reference circle (x ₀ , y ₀ , z ₀ ) and a three-direction rotation angle (θ, φ, γ) are obtained.

[Table 2]

(Equation 13)

[Equation 14]

(Equation 15)

(Equation 16)

[Equation 17]

(Equation 18)

An analysis method according to a second aspect embodies the concept of the analysis method according to the first aspect.

According to a third aspect of the present invention, in the six-degree-of-freedom motion analysis method according to the second aspect, a plurality of sets of the reference points are formed on the reference circle as a set of three points. Applying the calculation method according to claim 2 to a reference point, the spatial parameters (x ₀ , y ₀ , z ₀ ) for the reference circle,
(Θ, φ, γ) is calculated for the number of sets, and the spatial parameters of the corresponding number of sets are averaged to obtain one set of spatial parameter summary values. The (x, y, z) coordinates of each of the plurality of sets of reference points are newly calculated by substituting numerical values obtained by shifting the parameter outline values by minute increments, and a first circle having a predetermined minute radius is drawn around the points. On the other hand, a second circle having the same minute radius as the first circle is drawn around the same reference point on the image, and the overlapping area between the first circle and the second circle is obtained for all the reference points. Is determined in such a manner as to maximize the sum of, and correction is performed from the summary value.

[Equation 19]

(Equation 20)

(Equation 21)

(Equation 22)

(Equation 23)

(Equation 24)

According to this analysis method, by using a plurality of sets of the reference points, it is possible to improve the measurement accuracy as compared with a case where there are only three reference points (one set). Claim 3 also describes how to derive a minimum error result from data obtained for a plurality of sets of reference points.

[0014] The invention according to claim 4 is the invention according to claims 1 to 3.
In the six-degree-of-freedom motion analysis method described in any one of the above, the rigid body is provided with a cylindrical body having a reference circle on a side surface.

As described in this analysis method, it is easy to install a cylindrical body on a rigid body, and a reference circle can be provided with high accuracy.

According to a fifth aspect of the present invention, in the six-degree-of-freedom motion analysis method according to the fourth aspect, a plurality of reference circles are formed on a side surface of the cylindrical body.

According to this analysis method, since a plurality of reference circles are provided, it is possible to improve the measurement accuracy, particularly for the rotation angle of the rigid body.

The invention according to claim 6 is the invention according to claims 1 to 5
In the six-degree-of-freedom motion analysis method according to any one of the above, the position of the center of gravity of the rigid body is sequentially determined from the distance from the center of gravity of the rigid body to the center point of the reference circle, and the calculation result obtained for the reference circle. It is characterized by calculating.

In general, the reference circle is separated from the center of gravity of the rigid body. However, according to this analysis method, the motion of the center of gravity of the rigid body that the user wants to know most can be described. The acting aerodynamic force can be determined.

[0020]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, a comparative experiment on a 6-DOF motion analysis method for a rigid body based on image data from one direction proposed in the present invention is compared with a conventional method using image data from two directions. This will be described in detail including the results.

According to the present invention, a method for analyzing the motion of a falling rigid body which performs an unsteady motion by receiving pneumatic force by using only image data from one direction is established for the purpose of knowing the momentary force acting on the falling rigid body. Aimed at. Furthermore, using this method, the motion analysis of a rigid body that freely moves in an air flow was performed.
The motion handled in the present invention is a motion having a total of six degrees of freedom, including three degrees of freedom in translation of space and three degrees of rotation around each axis. As a specific object to be analyzed, a quadrangular pyramid-shaped rigid body was used, which was allowed to fall freely in the airflow vertically upward, and the movement (coordinate values and rotation angle) at that time and the aerodynamic force acting on it , And analyzed the moment.

[Principle of Analysis Method Based on Image Data from One Direction] When the measurement object is a rigid body, the relative positional relationship between a plurality of points (reference points) provided on the rigid body does not change during the movement of the rigid body. . Therefore, the correlation theory [see Reference 5] is applied to a group of reference points (measurement points) on an image (xz plane) photographed from one direction, and a 6-DOF motion analysis of a rigid body is performed.

As shown in FIG. 1, in this embodiment, a reference circle 10 is used as a model for applying a correlation. A reference point 20 is provided on the circumference of the reference circle 10. For example, a reference circle 10 located on the xy plane as an initial position is turned into an angle γ around the z-axis as shown in FIG. 1A, an angle φ around the x-axis as shown in FIG. As shown, the image is sequentially rotated by an angle θ about the y-axis. After that, it is assumed that the reference point 20 on the image is obtained by being translated in each axis direction. Here, as shown in FIG. 2, three reference points A installed on the circumference of the reference circle 10
After rotating (20a), B (20b), and C (20c) around each axis, the coordinate values of x and z at each point are given by equations (1) to (4).
It can be expressed as (6). Here, x ₀ and z ₀ indicate the center coordinates of the reference circle 10, and r indicates the radius of the reference circle 10.
Using the equations (1) to (6), x ₀ , y ₀ , r, γ, θ
Is solved, the above equations (7) to (12) are obtained. The remaining parameter φ can be obtained directly from the measured image data as the angle formed by the long axis of the ellipse formed by inclining the reference circle 10 and the x-axis. In shooting from one direction, the displacement in the depth (y-axis) direction cannot be directly measured.
In the present invention, the reference circle 10 that changes with the displacement in the depth direction is used.
Using the radius r of That is, the relationship between the amount of displacement in the depth direction and the contraction rate R = (r / r ₀ ) obtained by dividing the value of the radius r of the reference circle on the image by the actual dimension r ₀ is obtained in advance, and is obtained from the image data. The displacement (y) in the depth direction is determined from the contraction rate R. FIG. 3 shows an example of the relationship between the displacement (y) in the depth direction and the shrinkage ratio R obtained in advance. A linear relationship is established between the displacement (y) and the contraction rate R, and it can be seen that the displacement (y) in the depth direction can be obtained from the contraction rate R.

For measurement using image data, a plurality of sets of reference points 20a, 20b, and 20c having a positional relationship shown in FIG.
The average of the respective spatial parameters obtained from the equations (7) to (12) is set as a summary value. Since the same displacement and rotation can be given to each point by the formulas (1) to (6), each parameter is changed in small steps from the outline value, and the position of each point obtained by calculation is determined by image data. The displacement / rotation angle when the position is closest to the position coordinates of the point is defined as a solution. As a criterion for the closest approach, a first circle having a radius of 2 pixels centered on the reference point position obtained by calculation is drawn, while a second circle having the same radius of 2 pixels is drawn centered on the same reference point on the image. , The overlapping area (correlation value) of the first circle and the second circle is obtained for all the reference points, and the displacement and the rotation angle when the sum is maximum is obtained. This is because the displacement and the rotation angle are determined with higher accuracy by using a plurality of sets of reference points.

[Experiment Outline] FIG. 4 shows a cylindrical body 2 installed on a rigid body for analysis by photographing from one direction. On the cylindrical body 2, three reference circles 11, 12, 13 are provided,
A total of 48 reference points were placed on each circumference at 16 intervals at π / 8. The distance between the reference circles was 30 mm. In the image data measurement, three reference points at intervals of π / 4 on the reference circle 12 and three reference points at positions obtained by rotating the three reference points by π / 8 are similarly separated by 30 mm up and down. A total of 18 reference points including the reference points on the circumference of the reference circles 11 and 13 were used for the analysis of the correlation. The movement of the rigid body is performed by two video cameras 5.6 (SONY
And TRV9, TRV5 (registered trademark)) were installed with their optical axes orthogonal to each other and photographed (see FIG. 9). In the analysis method devised this time, only one video camera is required. In this experiment, the reason why two units were installed was to compare the analysis result with the conventional method using image data from two directions. Here, 18 reference points (x,
z) Six kinds of solutions can be obtained for the coordinates by the above equations (7) to (12), and the average value thereof is set as the outline value. Since the same displacement and rotation can be given to 18 points by the above equations (1) to (6), each displacement is changed in small increments from the outline value, and the positions of the 18 points calculated are measured by image data. The displacement / rotation angle at which the position coordinates become closest to the position coordinates of the 18 points was determined.

FIG. 5 shows a quadrangular pyramid 1 used as a specimen for the drop experiment. The quadrangular pyramid 1 has a square bottom surface with a side of 220 mm, an apex angle of 120 °, a material of aluminum, and a mass of 330 g. A reference point for image data analysis is provided on the quadrangular pyramid 1. That is, 2
A spherical marker 3 for the conventional method using a single camera, and a cylindrical body 2 and a reference circles 11, 12, and 13 for a method by imaging from one direction, and reference points are set on each reference circle. In the experiment, this quadrangular pyramid 1 is released into the airflow, but in order to prevent breakage when it deviates from the airflow and collides with a wall, a nylon thread with a diameter of 0.3 mm is used so as not to affect the movement. It is attached. During the experiment, the nylon yarn was in a warped state, and it was determined that the effects of the yarn mass, tension, and the like were negligible.

[Measurement of the position of the center of gravity] The position of the center of gravity of the quadrangular pyramid 1 was measured using an image as shown in FIG. Rigid and suspended in a suitable point, when superimposed on the vertical line, the center of gravity C _G Rigid located on the vertical line. This was performed from different directions, and the position of the center of gravity was measured. FIG. 7 shows the position of the center of gravity thus determined.

[Calculation of Moment of Inertia] The moment of inertia about the ζ axis passing through the center of gravity of the rigid body is determined experimentally from the period of a single vibration about a certain fixed axis that does not pass through the center of gravity and is parallel to the ζ axis. That is, the {moment of inertia I around the axis of a rigid body regarded as a double pendulum is M, the mass of the rigid body is M, the distance between the center of gravity and the fixed axis is d, the period of a simple vibration around a fixed axis is T, and the gravitational acceleration is g. Then, it is given by the following equation (13).

(Equation 25)

In order to obtain the moments of inertia I _X , I _Y , and I _Z around the X, Y, and Z axes passing through the center of gravity of the quadrangular pyramid 1, a simple vibration about a fixed axis parallel to each axis away from the center of gravity is obtained. Then, the cycle of vibration was obtained. When the quadrangular pyramid 1 is viewed from the lateral direction,
Since the shapes are the same in the X-axis and Y-axis directions, I _X = I _Y. The period T _X of the vibration about the fixed axis parallel to the X axis at 0.110 m away from the center of gravity is 0.736 sec, M = 0.330 kg, d ₁ =
Since it is 0.110 m, the moment of inertia about the X axis and the Y axis is I _X = I _Y = 4.87 × 10 ⁻³ kgm ² . Further, the period T _z about the fixed axis parallel to the Z axis at a distance of 0.56 m from the center of gravity is 0.733 sec, and M = 0.330 kg, d
Since at ₂ = 0.056 M, inertia moment about the Z-axis becomes ^{_{I z = 2.47 × 10 -3 kgm}} 2. Therefore, it was found that the moment of inertia of the quadrangular pyramid 1 was relatively larger in the pitching direction than in the yawing direction.

[Experimental Apparatus] In the drop test of the rigid body, as shown in FIG. 9, the free fall was simulated by releasing the quadrangular pyramid 1 into the airflow of the wind tunnel 4 having the outlet vertically upward.
The wind tunnel exit was 495 x 495 mm in size, and the wind speed was adjusted by opening and closing a bypass provided in the middle of the wind path. In addition, a honeycomb and a mesh for rectification are installed upstream of the wind tunnel outlet. Prior to the experiment, the wind speed distribution in the measuring section was examined. FIG. 8 shows the result. The wind speed was measured using a Pitot static pressure tube and a Göttingen manometer.
Measured at m and 22 cm. As a result, it was found that a flat wind speed distribution was obtained almost all over the exit of the wind tunnel, and that a drop test could be simulated.

As shown in FIG. 9, the state of the exercise was photographed using two digital video cameras 5 and 6 (manufactured by SONY, TRV5 and TRV9 (registered trademark)). However, as described above, what is necessary for the analysis method according to the present invention is one of them.
It is a stand. The video cameras 5 and 6 were installed using sights so that the respective optical axes coincided with the X axis and the Y axis of the absolute coordinate system. The heights and directions of the reference points corresponding to the origins in the sight were made to coincide with each other, and the two camera optical axes were installed orthogonally by capturing the reference points at the center of the image. The two digital video cameras 5 and 6 can use a remote controller to start recording at the same time, and use a stroboscope 7 to time-synchronize image data from two different directions.

[Expression of Rigid Body Motion] [Static Coordinate System and Coordinate System Fixed to Rigid Body] When describing the motion of a rigid body, for example, acceleration and force are calculated based on the displacement from the absolute coordinate system. In this experiment, since a rigid body that moves with six degrees of freedom is analyzed, six parameters are required to describe the position and orientation of the rigid body. That is, the translational displacement of the rigid center of gravity from the origin of the absolute coordinate system, and the rotation angle around each axis passing through the center of gravity. Therefore, when measuring the quadrangular pyramid 1, the X, Y, and Z axes were defined as shown in FIG. The absolute coordinate system, quadrangular pyramid body 1 has a position where definitive centroid C _G was suspended nylon yarn as the origin in still air, when determining the rotational displacement is Z axis to each axis of the absolute coordinate system → X axis → Y
The rotation was performed in the order of the axes, and the displacement was determined when the posture coincided with the posture of the photographed quadrangular pyramid. Further, the displacement around a coordinate axis in which the coordinates were fixed to the quadrangular pyramid, that is, the body axis was also obtained. In this method, the posture of the rigid body was obtained as displacements around each axis of the absolute coordinate system, and then converted into displacements around the body axis.

[Derivation of Acceleration Using Function Approximation] The motion of a rigid body is measured using an image, a potentiometer, or the like, and when a change in the position is obtained in a time series, the acceleration and force are calculated therefrom. One method is the difference method. As an example, the center difference of the fourth order accuracy that gives the acceleration second derivative (second derivative) at a certain time is given by the following equation (14).

(Equation 26) Here, u _j−2 , u _j−1 , u _j , u _{j + 1} , and u _{j + 2} are values obtained in time series, h is a time interval, and O (h ⁴ ) is an error. . Generally, measured values... U _j−1 , u _j , u _{j + 1} ... Include errors, and when the time interval h is relatively small, the errors may increase due to differences. FIG. 11 shows the result of measuring the position of the rigid body at a time interval of 5 ms using a potentiometer and performing the center difference with the fourth order accuracy [see Reference 7]. The obtained acceleration exhibits an unnatural vibration, which is inconvenient for deriving and analyzing the force. Here, the measured value used for the difference is skipped by one data such as u _j-4 , u _j-2 , u _j , u _{j + 2} , u _{j + 4} so that the time step width becomes 2h. By performing the difference with reduced time resolution, the vibration can be considerably suppressed.
FIG. 12 shows the time intervals of the differences as 1/5 (5Δt), 1/8 (8Δt), 1/10
(10Δt), 1/15 (15Δt). The vibration is suppressed as the time interval increases, but the peak value is also flattened at the same time. The optimal time step size is also an issue for the future.

As another method, an attempt was made to use Fourier analysis in which a difference is applied after filtering. That is,
Fourier transform is performed to remove high-frequency components, and a trajectory filtered by inverse Fourier transform is obtained. But,
The difference result of the trajectory after the filtering exhibits oscillation depending on the sampling frequency as before (FIG. 1).
3).

Therefore, the motion of the rigid body was considered to be continuous and smooth, and a function approximation was used. The trajectory of the movement is represented by a polynomial which is a continuous function, and the velocity and acceleration are obtained by differentiating the trajectory [see References 8, 9]. FIG. 14 shows a trajectory of a motion of a flat plate having a dihedral angle performing three degrees of freedom motion in a vertical plane in a drop simulation experiment. The order of the polynomial at the time of approximation can be up to one less than the number of data points.
This trajectory was expressed using polynomials of different orders of the 40th, 19th and 13th orders, and each was differentiated to derive the acceleration. In the expression of the trajectory, there was little difference due to the order of the polynomial, but there was a difference due to the order in the derived acceleration. This is shown in FIG. The acceleration obtained by differentiating the 40th-order polynomial diverges in the latter half and exhibits an unnatural vibration. This is considered to be due to the expression of the locus including even a slight error in the data. The accelerations from the 19th and 13th order polynomials have no unnatural vibrations and both draw well-matched curves. Therefore, it is understood that it is necessary to select an appropriate order also when performing a function approximation using a polynomial. In this experiment, it was concluded that an order of about 1/3 to 1/2 of the number of data points to be approximated was appropriate. The standard deviation s of the approximated polynomial with respect to the experimental value is as shown in the following table for each approximate order.

[Table 3]

[Experimental Results and Discussion] The quadrangular pyramid 1 is opened in the airflow vertically upward, falls slowly while vibrating like a pendulum, and then floats in the air in balance with the aerodynamic force (resistance). (FIG. 16). During this time, the nylon thread (diameter 0.3 mm) attached to prevent breakage when the quadrangular pyramid deviated from the airflow remained loose, so the effect of the tension and mass of the thread on the movement was considered to be minimal and can be ignored. . The wind speed at the time of the experiment was 10.1 m / s, and the Reynolds number, which was the representative length of the base of the quadrangular pyramid, was 1.6.
× 10 ^5.

[Results of Measurement from Two Directions] On the quadrangular pyramid 1, a conventional spherical marker 3 for measurement from two directions is provided.
There are eight points (only four points are shown) and are arranged to form a square. In the image data analysis, three points that can correspond to each other are detected in image data from two directions, and a slight correction is applied to the positions (details omitted). The position and orientation of the quadrangular pyramid 1 are calculated based on the positions of the plurality of spherical markers 3 with which correspondence has been obtained, and the locus of movement is obtained. FIG. 17 shows the locus of the center of gravity of the quadrangular pyramid 1 in the XZ plane. The quadrangular pyramid 1 descends while relaxing its falling speed, receives the aerodynamic force, balances the force with the gravitational force, and then sees that the aerodynamic force slightly wins and rises. 18 and 19 show the time change of the posture of No. 1. FIGS. 18 and 19 also show the result of function approximation of the trajectory by a polynomial in order to calculate the force acting on the quadrangular pyramid 1. With regard to the displacement in the translation direction, the vibration in the X and Y directions is performed while slightly reducing the amplitude.
It gradually descends and rises in the direction. From this, it can be seen that the quadrangular pyramid 1 falls while gently oscillating, and floats while attenuating the vibration by aerodynamic force.

FIG. 21 shows the change over time of the attitude of the quadrangular pyramid 1 in the body axis coordinates as shown in FIG. The displacement in the body axis coordinate is a change amount in which the body axis is coordinated from a certain image to the next image calculated from the image, and is therefore indicated by the speed at that time.

[Results of Measurement from One Direction] As a new method of image data analysis, a method of clarifying the six-degree-of-freedom movement of a rigid body from image data of only one direction has been devised.
The result of applying this method to the above-described movement of the quadrangular pyramid 1 will be described below. A cylindrical body 2 is provided on the quadrangular pyramid 1 for position measurement from one direction. Reference circles 11, 12, and 13 are formed on the cylindrical body 2, and each reference circle has a plurality of reference points. The angle, diameter, and reference point position of the cylindrical body 2 are measured, a displacement with six degrees of freedom is obtained, and a correlation method is applied based on the obtained displacement. With respect to the position of the reference point obtained by the image data measurement, equations (1) to (6)
Is used to change the reference point position in the calculation by giving a minute displacement. A circle having a radius of 2 pixels is assumed for each of the reference point by measurement and the reference point by calculation, and the average value of the overlapping area ratio is set as the correlation value s. The displacement when the correlation value s is the highest, that is, when the respective reference points overlap best, is adopted. FIG. 22 shows the correlation value s, which shows a low correlation value immediately after the start of exercise. This is probably because the quadrangular pyramid 1 was intensely moved immediately after entering the airflow, and the reference point was slightly blurred on the image. FIGS. 23 and 24 show the translational displacement, the rotational displacement, and the trajectories obtained by approximating the translational displacement and the rotational displacement. Although the error in the Y-axis direction, which is the measurement direction, is relatively large, it indicates that displacement in space can be obtained even by measurement from one direction.

[Calculation of aerodynamic force using polynomial] The main force acting on the rigid body during the falling motion in the airflow is gravity and aerodynamic force. In this experiment, as shown in FIG. 9, a fall simulation was performed in an airflow directed vertically upward, and an image was taken by one of the digital video cameras 5 and 6 fixed on the ground. Therefore, when the falling rigid body has a stable posture due to the balance between the aerodynamic force and the gravity, the motion in the screen becomes gentle, and the acceleration derived therefrom becomes small. That is, the force derived by the image data analysis in this experiment indicates the balance between the gravitational force acting on the rigid body and the aerodynamic force, and the aerodynamic force is small when the falling motion is stable.

The trajectory of the movement of the quadrangular pyramid 1 in the absolute coordinate system obtained by the image data measurement uses function approximation,
By differentiating a continuous function represented by a polynomial and having waveforms shown in FIGS. 18, 19, 23, and 24, acceleration can be obtained without unnatural vibration and aerodynamic force acting on a rigid body can be calculated. . FIG. 25 shows the result. It can be seen that a relatively large force acts in the Y direction in the first half of the dropping motion and a force acts periodically in the X direction. Further, although a periodic force acts also in the X direction, its attenuation is extremely small.
The fluctuation of the force in the Y and Z directions is relatively small in the latter half of the movement compared to the X direction. From this, it can be seen that the movement of the quadrangular pyramid transitions to a stable falling posture while slowly taking time in the lateral direction.

The forces and moments acting on the quadrangular pyramid were also calculated from the displacement on the coordinate axis fixed on the fuselage, that is, the coordinate of the fuselage axis. The displacement in the body axis coordinates is expressed using a polynomial, differentiated to derive the acceleration, the mass of the pyramid,
Force and moment were calculated from the moment of inertia around each axis. When the velocity and angular velocity of the rigid body are described in the moving coordinate system, it is necessary to consider that the direction of the coordinate axis also changes with time. As shown in FIG. 26, the moving coordinate components of the velocity V and the angular velocity ω are U, V, W and P, Q, R, respectively, the rigid body mass is m, and the moment of inertia about the X, Y, and Z axes is I _xx. , I _yy , I _zz , XY plane,
The products of inertia on the YZ plane and the ZX plane are represented by I _xy , I _yz , I
_zx . In the dynamic coordinate system, the force F acting on the center of gravity and the moment G around the axis are represented by the following equations (15) to (2).
0).

[Equation 27]

[Equation 28]

(Equation 29)

[Equation 30]

(Equation 31)

(Equation 32)

FIG. 27 shows the aerodynamic force acting on the quadrangular pyramid in the body coordinate system, derived from the above relationship. It can be seen that a relatively large force acts immediately after the start of the movement in the x and y directions to attenuate the lateral movement at the time of the falling movement, and that the cone has floated by the force applied in the z direction. In addition, the moment is attenuated while acting periodically, and it can be seen that the falling motion of the cone eventually becomes a stable posture.

[Discussion] In the past research, a rectangular flat plate and a flat plate having a dihedral angle have been treated in a three-degree-of-freedom drop motion experiment in a vertical plane. According to this, when a flat plate has a dihedral angle, its motion and angular velocity are both immediately attenuated and a stable falling posture is obtained as compared with a rectangular flat plate. The reason why the falling object was the quadrangular pyramid 1 in conducting the drop experiment was that the motion was predicted to be attenuated due to the dihedral effect and to fall stably.

From the results of the experiment, it was confirmed that the falling motion of the quadrangular pyramid 1 shifted to a stable posture.
The damping speed is different from that of a flat plate having a dihedral angle. In the case of a flat plate having a dihedral angle, the flat plate that has entered the airflow rapidly attenuates in one or two pitching motions, and accordingly the translation speed also attenuates, resulting in a stable falling posture.
On the other hand, in the case of the quadrangular pyramid 1, FIG.
As shown in FIG. 4, while the angular displacement shows a tendency to attenuate, the vibration does not stop during the observation, and rises while gently vibrating. The reason for this is that there is not much difference between the front projection areas of the two (flat plate: 220 × 150 mm ² , cone: 220 × 220 m
m ² ) Despite the fact that the moment of inertia around the pitching motion axis is one digit different (flat plate: 3.77 × 10 ^-4 kgm ² ,
A square pyramid; 4.87 × 10 ⁻³ kgm ² ) is considered. FIG.
As shown in (b), the angular displacement of the quadrangular pyramid 1 around the x and y axes repeats the vibration in substantially the same phase, so that the quadrangular pyramid 1 is rotated around the ridge line. You can see that it was. Further, from FIG. 27B, the yaw axis (z axis)
Since only a small moment acts on the periphery, the yawing is not attenuated, and it can be seen that the quadrangular pyramid 1 floats while rotating around the vertical axis.

[Summary] A method for analyzing motion from image data captured by one camera was devised, and compared with a conventional method using two cameras.
Whereas the conventional method is a method of correcting a position using image data from two orthogonal directions using two cameras, the method of the present invention occurs with a change in depth in a shooting direction. This is a method based on image data from one direction that utilizes a change in size, and uses the correlation of reference points on a rigid body. In this experiment, the falling motion of the quadrangular pyramid 1 having an apex angle of 120 ° was analyzed. The experiment simulated a fall by releasing an object in an airflow directed vertically upward, and realized a 6-degree-of-freedom falling movement without any restraint on movement by a displacement detection mechanism or a lead wire for signal extraction.

In order to calculate the aerodynamic force acting on the rigid body with higher accuracy based on the displacement obtained from the image data, the displacement of the rigid body was approximated by a function by a polynomial. That is, the motion is considered to be continuous and smooth in order to avoid unnatural vibration of the solution generated by the difference method. This was differentiated to calculate acceleration and further force. As a result, the falling motion of the quadrangular pyramid 1 vibrates while gradually rotating in the horizontal direction like a pendulum and falls while oscillating, but the vibration is attenuated by the aerodynamic force. However, the degree of this attenuation was poor, and it was found that the air force and the gravity gradually shifted to a stable falling posture over time. Motion was also described by displacement in the body axis. As a result, the movement of the quadrangular pyramid 1 like a pendulum has an axis in the direction of its ridge, the attenuation is gentle, and no moment acts to attenuate the rotation in the yaw direction. It turned out that he came up.

As is apparent from FIGS. 18 and 19, the six-degree-of-freedom motion analysis method based on image data from one direction according to the present invention has a good correlation with the conventional method based on image data from two directions. As shown, it was found that comparable analysis accuracy was obtained.

[Reference List] [Reference 1] Urita, A., Nakamura, Y and Kawazoe, H., Ame
asurement of Freely Oscillating Body Subject to Ae
rodynamic Forces, AIAA Paper94-2612, 1994. [Reference 2] Urata, Nakamura, Kawazoe, Pressure distribution around a re-entry object pendulum moving in vertical flow, Journal of the Japan Society for Aeronautical and Space Sciences, Vol.
44, No. 515, pp 729-734, 1996. [Reference 3] Tanaka, Optical Non-contact Three-Dimensional Motion Measurement Method in Aquarium Test, Ishikawajima Harima Technical Report, Vol.25, No.4, pp.1-7,
1985. [Literature 4] Arima, Kawazoe, Obayashi, Matsumoto, Image analysis of falling motion of flat plate with dihedral corner, Proc. Of the 36th Annual Meeting of Chugoku-Shikoku Branch of the Japan Society of Mechanical Engineers, 1998. [Reference 5] Obayashi, Kawazoe, Arima, Matsumoto, Motion Analysis of Falling Plate by Image Collection of 29th Annual Meeting of the Japan Aerospace Society,
1998. [Reference 6] Analytical photogrammetry, edited by the Japan Society of Photogrammetry, 1989. [Reference 7] Obayashi, Kawazoe, Matsumoto, Yoshino, Posture stability of a falling object, Proc. [Reference 8] Kawazoe, H., Ohbayashi, M., Arima, K., Matsu
moto, M., Calculationof Aerodynamic Forces Acting
on Falling Object with Video Movie, Proceedings of
VSJ-SPIE '98, ABO23 [Reference 9] Kawazoe, H., Arima, K., Ohbayashi, M., Matsu
moto, M., Video PictureAnalysis on Falling Motion o
f Dihedral-Ang1e Plate with Three Degree of Freedo
m, AIAA Paper, No.99-0292

[0050]

As described above, according to the present invention,
Since the motion analysis of a rigid body can be performed based on image data taken from only one direction, not only does it have no effect on the motion of the rigid body in a non-contact manner, but also requires imaging from two directions. The method eliminates the need to synchronize two cameras, simplifies measurement, and halves the cost of expensive high-speed cameras. The accuracy of the analysis is comparable to that of the conventional method.

[Brief description of the drawings]

FIG. 1 is a diagram illustrating a definition of a rotation direction of a reference point provided on a reference circle.

FIG. 2 is a diagram illustrating three reference points on a reference circle.

FIG. 3 shows an image when the reference circle is displaced in the y-axis direction.
Radius r and real radius r ₀Ratio (shrinkage ratio R = (r /
r₀)) And the result of calibrating the relationship between y-axis position
FIG.

FIG. 4 is a perspective view showing three reference circles provided on a cylindrical body and reference points provided on each reference circle.

FIG. 5 is a perspective view showing a quadrangular pyramid used in the experiment, and a cylinder, a reference circle, and a reference point installed on the pyramid.

FIG. 6 is a diagram illustrating a method of measuring the center of gravity of a quadrangular pyramid used in an experiment.

FIG. 7 is a side view showing the shape of the quadrangular pyramid used in the experiment and the position of its center of gravity.

FIG. 8 is a graph showing measurement results of a wind speed distribution at the exit of an experimental wind tunnel.

FIG. 9 is a perspective view showing a state of an image data acquisition experiment set including a conventional two-way image method.

FIG. 10 is a diagram illustrating definitions of an absolute coordinate system and a body axis coordinate system.

FIG. 11 is a graph showing an acceleration calculation result by a difference method.

FIG. 12 is a graph showing a calculation result of acceleration improvement by a difference method.

FIG. 13 is a graph showing time-axis changes in x-direction displacement and acceleration by FFT analysis.

FIG. 14 is a graph showing a change in x, y, and θ with respect to time on the basis of a 40th-order polynomial approximation.

FIG. 15 is a graph showing calculation results of acceleration / angular acceleration by 13th, 19th, and 40th order polynomial approximations.

FIG. 16 is a diagram showing a state of a falling motion of a quadrangular pyramid.

FIG. 17 is a graph showing a locus of a quadrangular pyramid center of gravity in an xz plane.

FIG. 18 shows a time axis change of position coordinates (one-way image method and 2
7 is a graph showing a comparison with the directional image method).

FIG. 19 is a graph showing a time axis change of the rotation angle (comparison between the one-way image method and the two-way image method).

FIG. 20 is a diagram illustrating the definition of a body axis coordinate system.

FIG. 21 is a graph showing changes in the speed / angular speed time axis of the quadrangular pyramid based on the body axis coordinate system.

FIG. 22 is a graph showing a change in the correlation value s over time.

FIG. 23 is a graph showing a free fall motion (x, y, z) of a quadrangular pyramid by a one-way image method.

FIG. 24 is a graph showing the free fall motion (θ, φ, ψ) of the quadrangular pyramid by the one-way image method.

FIG. 25 is a graph showing a time axis change of a force acting on a quadrangular pyramid.

FIG. 26 is a diagram illustrating definitions of forces and moments in a body axis coordinate system.

FIG. 27 is a graph showing a time axis change of a force and a moment acting on a quadrangular pyramid.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Square pyramid (rigid body) 2 Cylindrical body 3 Spherical marker 4 Wind tunnel 5.6 Digital video camera 7 Stroboscope 10.11.12.13 Reference circle 20 Reference point 20a Reference point A 20b Reference point B 20c Reference point C

──────────────────────────────────────────────────続 き Continued on the front page (51) Int.Cl. ⁷ Identification code FI Theme coat ゛ (Reference) G06T 7/00 G06F 15/62 415 F Term (Reference) 2F065 AA04 AA17 AA39 AA54 BB05 BB24 DD00 FF04 FF64 JJ03 JJ16 JJ26 QQ26 5B057 CH08 DA07 DB03 DC06 DC08

Claims (6)

[Claims] A reference circle is provided integrally with a rigid body, at least three reference points are formed on the reference circle, and an image of the reference point is fixed during spatial movement of the rigid body. The center coordinates and the rotation angle of the reference circle are sequentially calculated from the image data of the reference circle and the reference point, which are intermittently photographed at minute time intervals using a camera, and are obtained from the image data of the rigid body. A 6-DOF motion analysis method characterized by analyzing translational motion with 3 DOF and rotational motion with 3 DOF. 2. Referring to the image data and symbols defined in the following table, three reference points are selected from the at least three reference points to form one set, and one set of three reference points is selected. Each (x, z) coordinate and φ, which is the angle between the major axis of the ellipse formed by tilting the reference circle and the x axis, are obtained, and these values are sequentially calculated by the following equations (7) to (12). Substituting and further calculating the calculated radius r of the reference circle and the pre-calibrated contraction rate R
, Y ₀ is obtained from the coordinates, the center coordinates (x ₀ , y ₀ , z ₀ ), which are the six spatial parameters of the reference circle, and the three-directional rotation angles (θ,
2. The method of claim 1, wherein (φ, γ) is obtained. [Table 1] (Equation 1) (Equation 2) (Equation 3) (Equation 4) (Equation 5) (Equation 6) 3. A plurality of sets of the reference points are formed on the reference circle as a set of three, and the calculation method according to claim 2 is applied to the reference points of each set, so that The spatial parameters (x ₀ , y ₀ , z ₀ ) and (θ, φ, γ) are calculated for the number of sets, and the spatial parameters of the corresponding number of sets are averaged to obtain a set of spatial parameter summary values. By substituting a numerical value obtained by shifting the outline value of the spatial parameter by a small increment into the following equations (1) to (6), (x, y, z) coordinates of each of the plurality of sets of reference points are newly calculated, A first circle having a predetermined minute radius is drawn around a point, and a second circle having the same minute radius as the first circle is drawn around the same reference point on the image. Obtain the overlapping area for all reference points, and determine the minute increments in the previous period so that the sum of the overlapping areas is maximized 6 DOF motion analysis method according to claim 2, wherein the corrected from the summary value each. (Equation 7) (Equation 8) (Equation 9) (Equation 10) [Equation 11] (Equation 12) 4. The rigid body is provided with a cylindrical body having a reference circle on a side surface.
6. The 6-DOF motion analysis method according to any one of the above. 5. The six-degree-of-freedom motion analysis method according to claim 4, wherein a plurality of reference circles are formed on a side surface of the cylindrical body. 6. The position of the center of gravity of the rigid body is sequentially calculated from a distance from the center of gravity of the rigid body to the center point of the reference circle and a calculation result obtained for the reference circle. 6. The 6-DOF motion analysis method according to any one of 1 to 5.