JP7313054B2 - Method, apparatus and program for measuring dynamic friction coefficient - Google Patents

Description

The present invention relates to a method, apparatus and program for measuring dynamic friction coefficient.

The coefficient of dynamic friction is an index of the resistance acting in the opposite direction to the direction of travel when an object is sliding on a surface. With this value, the drag force can be predicted if the mass of the object is known.

F = μN
The magnitude of the resistance force F is expressed by the product of the weight N and the coefficient of dynamic friction μ. If the coefficient of dynamic friction is constant, the resistance is constant. Therefore, in order to actually measure the coefficient of dynamic friction, force is actually applied to an object whose weight is known to cause it to slide, and the magnitude of the force applied at a constant speed is measured. This is because the speed is constant when the pulling force and the frictional force are in balance, so the frictional force can be determined by measuring the pulling force.

Therefore, conventionally, a technique for measuring the dynamic friction coefficient μ by the following method has been developed.
(Prior art 1)
The dynamic friction coefficient is obtained by placing an object on a surface and moving the surface sinusoidally in a one-dimensional direction and measuring the maximum speed of the object that follows the movement. This technique is a method of measuring the coefficient of dynamic friction used for the performance evaluation of seismic isolation devices for buildings in the construction industry. In prior art 1, instead of actually pulling an object and measuring the force at that time, the object is placed on a surface, the surface is moved sinusoidally in a one-dimensional direction, and the maximum speed of the moving object is measured.
(Prior art 2)
A curling stone on ice is pulled at a constant speed with a spring scale, and the dynamic friction coefficient is obtained by directly measuring the frictional force at that time.

However, while prior art 1 has the advantage of being able to handle large objects compared to the simplest method of pulling an object at a constant speed with a spring scale or the like, it is necessary to change the settings in terms of obtaining speed dependence, which is extremely time-consuming and difficult to obtain low-speed data just before stopping.

Also, in prior art 2, the frictional force of curling stones on ice is directly measured using a spring balance method, but it is difficult to prepare measurement conditions that maintain a constant speed, and it is particularly difficult to obtain data in the low-speed range.

In this way, the actual situation is that the method of measuring the coefficient of dynamic friction is realized by performing many steady methods.
The coefficient of dynamic friction is the most basic information for calculating the force required to move an object under conditions where friction works. In the framework of general physics, the dynamic friction coefficient is treated as a constant value, but it is also known that it actually changes depending on the load and speed. There is no theory that can predict them in a unified manner, and it is necessary to measure the friction force under actual conditions individually in engineering applications. In principle, it is easy to actually measure the frictional force, and it is sufficient to actually measure the force required to move an object at a constant speed using a spring scale or the like. However, setting the conditions for the experiment is not always easy.

On the other hand, Patent Literature 1 listed below describes a technique for simply measuring a force acting on an object using moving images. According to the technique described in Patent Document 1, a video frame image of an arm that constitutes a torsion scale to which an object is attached is generated, the center of gravity of the arm image of the video frame is determined, the rotation angle is obtained from the data of the center of gravity, and the force acting on the object is determined.

However, Patent Literature 1 does not disclose the use of moving images to measure the dynamic friction coefficient.

Japanese Patent No. 5578667

The present invention has been made in view of the above facts, and it is an object of the present invention to provide a method, apparatus, and program for extremely simply measuring the dynamic friction coefficient using moving images without directly measuring the frictional force.

In order to solve the above problems, the method for measuring the dynamic friction coefficient of the present invention acquires frames of still images arranged in time series of an object sliding on a surface, identifies the object in each of the frames, analyzes the image of the identified object, calculates the position of the object for each frame, calculates the speed of the object from the rate of change of the position of the object with time for each frame, calculates the acceleration of the object from the rate of change of the speed with time, calculates the acceleration of the object based on the acceleration of the object and the gravitational acceleration. and calculating the coefficient of dynamic friction on the surface of the object.

Preferably, the step of calculating the position of the object includes extracting each region of the object from each still image of the frame and calculating the position of the center of gravity of each region as the position of the object.
Preferably, identifying the object comprises recognizing features of the object. For example, the feature of the object is the color and/or shape of the object.

Also preferably, in the step of calculating the speed of the object, the speed of the object is calculated based on the ratio of the change in position of the object occurring between frames to the time between frames.
For example, the still image frames are captured at a constant frame rate.

More preferably, the step of calculating the acceleration of the object applies a least-squares method using a quadratic function to time-series data of the speed of the object, and calculates the acceleration as a quadratic coefficient of the quadratic function.

For example, capturing the still image frames may comprise filming the object with a video camera.
An apparatus for measuring a coefficient of dynamic friction according to another aspect of the present invention comprises a memory for storing frames of still images of an object sliding on a surface arranged in time series; an image recognition unit for identifying the object in each of the frames; a position calculation unit for analyzing the image of the identified object and calculating the position of the object for each frame; and a dynamic friction coefficient calculator for calculating the dynamic friction coefficient on the surface of the object based on the acceleration of the object and the gravitational acceleration.

A program according to still another aspect of the present invention is configured to cause an information processing device to execute the above-described method for measuring the dynamic friction coefficient.
(Action and effect of the present invention)
The present invention is a technical means for measuring the dynamic friction coefficient of an object sliding on a smooth surface. Simply slide the object with an initial velocity on the surface, video record how it comes to a stop due to frictional force, and analyze the video to obtain the dynamic friction coefficient as a function of speed. It does not require all the hardware required to actually measure the frictional force by actively moving an object at a low speed, and the speed dependence can be measured in a single measurement. It is also easy to improve the accuracy by repeated measurements.

As a direct application, the coefficient of dynamic friction between the curling stone and the ice surface in a curling competition can be obtained very simply and instantaneously, along with the speed dependence, simply by taking a video of the curling stone being thrown and performing analytical calculations on the moving image using a computer. In the curling competition, the coefficient of dynamic friction fluctuates daily and is the most important quantity that determines victory or defeat.

In addition, in the braking performance of a vehicle, the coefficient of dynamic friction of tires is directly related to safety performance. This also makes it possible to easily measure the dynamic friction coefficient, which is the stopping ability as well as the speed dependence, simply by taking a video of the test vehicle slipping.

FIG. 1 is a functional block diagram of a dynamic friction coefficient measuring device according to one embodiment of the present invention. FIG. 2 is a flowchart of a dynamic friction coefficient measuring method using the dynamic friction coefficient measuring device of FIG. FIG. 3 is an image of a surface on which curling stones slide, (a) is a still image of a frame, and (b) is a still image of a frame when a curling stone of interest is identified and its position is calculated. FIG. 4 is a graph showing the trajectory of the center-of-gravity position of the curling stones. FIG. 5 is a graph showing the time variation of the velocity of the curling stone calculated from the position of the center of gravity of the curling stone in FIG.

An embodiment of the present invention will be described below with reference to the drawings.
FIG. 1 shows a functional block diagram of a dynamic friction coefficient measuring device 1 according to one embodiment of the present invention.同図に示されるように、動摩擦係数測定装置１は、面２０上を滑走する物体Ｏを所定のフレームレートでビデオ撮影するビデオカメラ２と、ビデオカメラ２からのデータを入力するための入力部３と、入力部３を通して入力されたビデオカメラ２のデジタル信号（或いはアナログ信号）をキャプチャーして動画データに変換するビデオキャプチャー部４と、動画データを時系列順に並べられた２次元の静止画のフレームに変換する動画／静止画変換部５と、２次元の静止画のフレームF ₁ ,F ₂ ,F ₃ ,……F _k ……を格納するメモリ６と、を備えている。

The video camera 2 can be a digital video camera, an analog video camera, a digital camera used in video mode, a mirrorless camera, a single-lens camera, or the like. A video camera provided in an information processing device such as a smart phone or a tablet can also be used as the video camera 2 .

The input unit 3 can be connected to the video camera 2 and can be implemented as an interface device (such as USB) for inputting signals from the video camera 2 . Alternatively, the input unit 3 can be configured by a reading device that reads moving image data from a memory (USB memory or SD card) storing moving image data captured by the video camera 2 (in this case, the video capture unit 4 can be omitted). That is, the configurations 2, 3, 4, 5, and 6 of the dynamic friction coefficient measuring device 1 can be any configuration that provides the dynamic friction coefficient measuring device 1 with still image frames F ₁ , F ₂ , F _{3 ,} .

A still image of each frame is given by the stationary two-dimensional light intensity I(x, y, t) at each position (x, y) of a rectangular area consisting of a total of m×n pixels, for example, m pixels on the horizontal side (x direction) and n pixels on the vertical side (y direction). Here, the x-coordinate value and the y-coordinate value are each represented by discrete values in units of pixels. Also, the time t is represented by a discrete value t= _{t 1 , t 2 ,} t _{3 ,} . . . t _k . The frame rate is determined by the specifications or settings of the video camera 2, and is, for example, 30 frames/second, but the present invention is not limited to this example.

When the still image of the frame is a color image, the still two-dimensional light intensity image I can be represented by luminance information I _R (x, y, t), _IG (x, y, t), and I _B (x, y, t) for each color of RGB.

In addition, the dynamic friction coefficient measuring device 1 stores a memory 7 storing information indicating the characteristics of the object O, and based on the characteristics of the object O stored in the memory 7, the frame F of the still image stored in the memory 6₁,F₂,F₃,……F_ka position calculator 9 that analyzes the image of the object O identified in each frame and calculates the position p of the object O; a speed calculator 10 that calculates the speed v of the object O based on the position p of the object O in each frame and the frame rate of the video camera 2; an acceleration calculator 11 that calculates the acceleration a of the object O based on the speed v of the object O and the frame rate; and a dynamic friction coefficient calculator 12 for calculating the dynamic friction coefficient μ(p, v) as a function of the speed v, and an output unit 13 for outputting the calculated dynamic friction coefficient μ.

The information indicating the characteristics of the object O stored in the memory 7 is, for example, the color, shape, pattern of the object O, or a combination of at least two of them. Frames F ₁ , F ₂ , F ₃ , _. Also, features such as shapes and patterns may be learned by machine learning, or a region D showing features of the object O may be extracted from a still image using techniques similar to face recognition, eye recognition, etc. used in digital cameras. Further, the contour of the object candidate is extracted from the still image, and the shape having a closed contour is compared with the shape of the object O stored in the memory 7, and the contour shape with a high degree of similarity may be identified as the object O.

As an example of the object O, an example of a curling stone gliding on the surface 20 is shown in FIG. 3(a). As shown, the curling stones O ₁ , O ₂ , and O ₃ are colored yellow or red, and the region D of the curling stones can be identified by color extraction.

The position calculation unit 9 performs image analysis on the area D of the object O identified in the two-dimensional still image of each frame, and calculates the coordinates of the representative point of the area D as the position p(x, y) of the object O. FIG. For the origin of the coordinates at this time, for example, the position when the object O starts sliding on the surface 20 can be selected, but it is not necessary to be limited to this, and any position on the surface 20 in the still image frame may be selected.

The representative point of the area D of the object O may be any point fixed on the object O among the pixels forming the object O on the still image. Most preferably, said representative point is the centroid of the area of object O. The position r _g (x _g , y _g ) of the center of gravity as the representative position of the object O is determined by the position calculator 9 as a position obtained by weighting and averaging the light intensity I (x, y, t) over arbitrary positions (x, y) in the region D using weighting coefficients, as shown in the following equation.

Alternatively, the position calculator 9 may calculate the center-of-gravity position from the luminance information of the pixels forming the contour of the area D instead of the pixel luminance information inside the area D as in the equation (1). Also, if the object O is colored with a certain characteristic color, such as red, the center of gravity position of the red object O can be derived by using the luminance information I _R (x, y, t) regarding red instead of I (x, y, t) in equation (1). Other colors or mixed colors of RGB can be similarly derived.

The position calculator 9 sets the center-of-gravity position r _g (x _g , y _g ) that satisfies the formula (1) as the position p of the object O as shown in the following formula.

In the case of the example of application to curling stones in FIG. 3(a), the position calculation unit 9 selects the lower left yellow curling stone _O1 by image recognition, and automatically calculates the position of the luminance centroid of the yellow color, as shown in FIG. 3(b). Note that the position calculator 9 converts the position p of the object O on the frame of the still image into an actual position on the plane 20 . For this conversion, for example, the distance from the origin to the object O on the still image is converted into the distance from the origin to the object O on the actual surface 20 according to the distance to the object O focused by the video camera 2 and the focal length of the lens of the video camera 2. Alternatively, the position calculator 9 may calculate the actual position of the object O from a scale having a predetermined size (for example, the diameter of the object O) captured in a still image.

The position calculation unit 9 performs the above image analysis on all still image frames and arranges them in order to obtain time-series data p ₁ , p ₂ , p ₃ , …… _pk …… of the position p of the object O in each frame. Each _piece of time-series data p _k ( _k =1 _, . FIG. 4 shows the trajectory of the center-of-gravity position of the curling stone _O1 shown in FIG. 3(b). In Fig. 3(b), it was possible to automatically measure how a curling stone thrown from the right side stopped while bending its trajectory.

The speed calculator 10 calculates the speed v of the object O from the time-series data p ₁ , p ₂ , p _{3 ,} . Since the frame rate of the exemplary video camera 2 is 30 frames/second, each point shown in FIG. 4 represents a position every 1/30th of a second. Therefore, the spacing between adjacent points, shown in FIG. 4, reflects speed. The rate of change of the position over time is the velocity, and the momentary velocity can be obtained from this trajectory information. Therefore, the speed calculation unit 10 can calculate the speed of the object O based on the ratio of the change in the position of the object O occurring between adjacent frames to the time between adjacent frames determined by the frame rate of the video camera 2.

That is, the speed calculator 10 can calculate the speed _vk of the object O at each position _pk by the following equation.

where _Fr is the frame rate (frames per second).
From the equation (3), it can be seen that the time series data _v1 , _v2 , _v3 , ... _vk of the speed v can be calculated from the time series data _p1 , _p2 , _p3 , ... _pk of the position p.

_The acceleration _calculator 11 calculates accelerations _a1 , _a2 , _{a3 , . . .}
That is, the acceleration calculator 11 can calculate the acceleration _ak of the object O at each position _pk by the following equation.

From the equation (4), it can be seen that time series data _a1 , _a2 , _a3 , ... _ak of acceleration a can be calculated from time series data _v1 , _v2 , _v3 , ... _vk of velocity v.
FIG. 5 is a time variation of the speed of the curling stone _O1 shown in FIG. That is, FIG. 5 shows the time change of the speed of the curling stone _O1 , and shows how the curling stone _O1 decelerates and eventually stops. Since the rate of change in speed is the acceleration, the acceleration can be obtained by obtaining the slope from this data.

Time-series data of the acceleration a can be obtained by analyzing the acceleration according to the definition of the differentiation of the equation (4), but the acceleration to be obtained is usually only the average acceleration when regarded as uniformly accelerated motion. For this reason, the most effective method for data analysis is to consider the position time series data p _k (k=1, .

In the method of least squares, the parameter in the theoretical formula that minimizes the value of χ ² defined by the following formula (5) is determined as the optimum value. In this case, the parameters correspond to zero-order, first-order, and second-order coefficients in the theoretical formula.

In addition, since errors can also be evaluated in this analysis, information specifying reliability and uncertainty can be obtained. The error in the least squares method is given as the range of parameters that increase the value of χ ² by 1 above the minimum value. In the quadratic function, these optimum values and errors are strictly analytically determined, and there is no need to perform special numerical calculations. The data range used for the least squares method can be selected from at least 3 points to all points depending on the purpose. The use of all points corresponds to uniformly accelerated motion, which is sufficient when the velocity dependence of the dynamic friction coefficient is not of interest, and provides the highest accuracy.

The dynamic friction coefficient calculator 12 calculates the dynamic friction coefficient μ on the surface 20 of the object O from the acceleration a calculated by the acceleration calculator 11 . Note that the coefficient of dynamic friction μ can be expressed as μ(p, v) since it can be a function of the position p and the speed v.

The deceleration is due to friction, since the forces acting on the object O sliding on the surface 20 are basically only frictional forces. The equation of motion of the object is
ma = - μmg (6)
, and the acceleration is opposite to the direction of travel of the object. That is, deceleration. Here, m is the mass of the object, μ is the dynamic friction coefficient, a is the acceleration, and g is the gravitational acceleration. Therefore, the dynamic friction coefficient, which is an unknown quantity, can be obtained by actually measuring the acceleration a.
μ=-a/g (7)
is asked directly.

The output unit 13 outputs the dynamic friction coefficient μ(p, v) calculated by the dynamic friction coefficient calculation unit 12 . For example, if the output unit 13 is a display, the display may display an image of the surface 20, the speed v, and the dynamic friction coefficient μ for each position p. Of course, it is not limited to this example, and the calculation result of the dynamic friction coefficient may be printed by a printer.

The dynamic friction coefficient measuring device 1 may be realized by a computer in which a program for executing the dynamic friction coefficient measurement described above is installed. The program is installed in a computer and executed, so that at least the functions of the image recognition unit 8, the position calculation unit 9, the speed calculation unit 10, the acceleration calculation unit 11, and the dynamic friction coefficient calculation unit 12 are sequentially executed on the frames of still images stored in the memory 6 of the computer. Of course, the program may further have a series of functions such as control of the input unit 3, video capture unit 4, moving image/still image conversion unit 5, output unit 13, and the like.

In addition, the computer that realizes the dynamic friction coefficient measuring device 1 can be realized not only by a personal computer such as a so-called notebook computer or a desktop computer, but also by an information processing device such as a smart phone or a tablet terminal. When a smartphone, a tablet terminal, or the like is equipped with a video camera, the dynamic friction coefficient measuring device 1 and the video camera 2 can be realized by one device.

Next, the flow of calculation of the dynamic friction coefficient by the dynamic friction coefficient measuring device 1 according to one embodiment of the present invention will be described with reference to the flowchart of FIG.
As shown in FIG. 2, object O is first slid on surface 20 (step 100). In step 100, for example, an initial velocity may be given to the object O to allow it to slide freely. Moreover, when the object O is a tire of a vehicle, the test vehicle on which the tire is mounted may be caused to slip. Alternatively, if the object O is heavy and difficult to launch with an initial velocity on the horizontal plane, the surface 20 may be tilted to allow it to slide by gravity. It is possible to take a video of the process from when a force exceeding the maximum static friction force is applied and when the slide starts to slide until it stops. Since the maximum static frictional force is greater than the dynamic frictional force, the inclination angle of the surface 20 can be set so as not to stop and accelerate.

Next, the object O sliding on the surface 20 is video-photographed by the video camera 2 (step 102). Still image frames F ₁ , F ₂ , F ₃ , . . . F _k .

Next, _the image recognition unit 8 of the dynamic friction coefficient measuring device 1 recognizes the object O in each still image of the frames F ₁ , F ₂ , F ₃ , .

Next, the position calculator 9 _of the dynamic friction coefficient measuring device ₁ analyzes _the regions of the object O identified in each of the frames _{F 1} , F ₂ , F _{3 ,} .

Next, the speed calculator 10 of the dynamic friction coefficient _measuring device 1 _calculates , as the speed v of the object O, the ratio of changes in the positions _{p1 , p2 , p3 ,} . As a result, time-series data v ₁ , v ₂ , v ₃ , . . . v _k .

Next, the acceleration calculator 11 of the dynamic friction coefficient measuring device 1 calculates the acceleration a of the object O from the time change of the speed v of the object O (step 110). At this time, the time series data _v1 , _v2 , _v3 , ... _vk of the speed v may be subjected to the least squares method using a quadratic function to calculate the time series data _a1 , _a2 , _a3 , ... _ak of the acceleration for each position p.

Finally, based on the acceleration a of the object O and the gravitational acceleration g, the dynamic friction coefficient μ(p, v) is calculated as a function of each position p and speed v using the equation (4) (step 112).
The present invention does not require any procedure for actively continuing the motion of an object, and can measure the dynamic friction coefficient at once up to an ultra-low speed region just before stopping just by taking a video of how the object slides freely with an initial speed. The time and cost of the measurement work can be reduced by an order of magnitude, and it is also possible to acquire data in the low-speed region that cannot be acquired by conventional methods. Furthermore, the coefficient of dynamic friction is not always constant depending on the location on the surface, such as on a large surface. The present invention can also acquire such sliding path dependency of the dynamic friction coefficient at once.

Let's take curling as an example. The information we want to obtain is the roughness of the bottom surface of each stone, the individual difference in dynamic friction coefficient on ice, and its velocity dependence. The information that the competitor needs is first the average value of the coefficient of dynamic friction under the conditions of the day, then its variation with position on the ice, the variation with the stone, and the velocity, that is, the variation with position until stopping. The ice conditions change from day to day and from hour to hour, and it is important to accurately grasp them.

Therefore, regardless of whether it is before the competition or during the competition, the video of the curling stone sliding is taken. The position of the curling stone is then calculated frame by frame by image analysis. At this time, the curling stone is colored yellow or red, and the position of the curling stone can be roughly estimated by color extraction. The center of gravity may be determined accurately after the feature is learned by machine learning and the position is approximated. The video information is usually continuous information of still images at 30 frames per second, and the positions of curling stones can be obtained with an accuracy of 30 per second. In principle, it is possible to follow the position with the naked eye, but it is not practical because of the lack of accuracy and the enormous amount of work involved. The present invention utilizes the high-accuracy position determination by image processing used in the prior invention, Japanese Patent No. 5578667, to measure the position of an object in a highly accurate and time-saving manner.

The present invention uses only a video camera 2 capable of capturing digital moving images, and a smart phone, a personal computer, or the like for analysis. Experiments do not require special measurements, just video shooting of the curling stone during the competition.

If the object can be slid freely, the dynamic friction coefficient can be obtained accurately only with a personal computer if the moving image can be taken. It does not require large-scale investment of equipment and can be quickly evaluated. In applications such as factories, it not only leads to significant cost reduction, but also improves reliability and shortens the evaluation period. In terms of curling competition support, it is effective as an IT support technology for sports because it is possible to obtain results from data acquisition immediately at the stadium.

The present invention has a wide range of applications, and can be used for evaluation of brake performance, performance evaluation of sporting goods such as skis, evaluation of seismic isolation structure, and evaluation of heat generation due to friction. For example, the present invention can also be used for evaluation of railroad panda graphs. In addition, while the coefficient of friction of a magnetic disk, which is the recording medium of a hard disk, is an important performance factor, a device such as a spring for measurement is currently used.

Furthermore, in the present invention, by combining the image analysis technology of the image recognition unit 8 and the high-precision position measurement technology of the position calculation unit 9, it is possible to measure the position of a moving object beyond the pixel resolution of a still image frame. Therefore, according to the present invention, it is possible to obtain with extremely high accuracy the dynamic friction coefficient of the surface on which the object slides based on the acceleration of the object obtained from the position of the object in each frame.

The above is one embodiment of the present invention, but the present invention is not limited to the above example, and can be arbitrarily and suitably modified within the scope of the present invention.
For example, formulas (1) to (5) can be changed as desired.

1 dynamic friction coefficient measuring device 2 video camera 3 input unit 4 video capture unit 5 video/still image conversion unit 6 memory for frames of still images 7 memory storing information of object O 8 image recognition unit 9 position calculation unit 10 speed calculation unit 11 acceleration calculation unit 12 dynamic friction coefficient calculation unit 13 output unit

Claims (15)

A method for measuring a dynamic coefficient of friction comprising:
Acquire time-ordered still image frames of an object gliding on a surface,
identifying the object in each of the frames;
analyzing an image of the identified object to calculate the position of the object for each frame;
calculating the speed of the object from the time rate of change of the position of the object for each frame;
calculating the acceleration of the object from the time rate of change of the speed;
calculating a dynamic friction coefficient on the surface of the object based on the acceleration of the object and the gravitational acceleration ;
A method according to claim 1, wherein the step of calculating the acceleration of the object comprises: applying a least-squares method with a quadratic function to time-series data of the velocity of the object, and calculating the acceleration as a quadratic coefficient of the quadratic function. 2. The method according to claim 1, wherein in the step of calculating the position of the object, each region of the object is extracted from each still image of the frame, and the position of the center of gravity of each region is calculated as the position of the object. 3. The method of claim 1 or 2, wherein identifying the object comprises recognizing features of the object. 4. The method of claim 3, wherein the feature of the object is the color and/or shape of the object. 5. The method of any one of claims 1 to 4, wherein calculating the speed of the object comprises calculating the speed of the object based on the ratio of the change in position of the object that occurs between frames to the time between frames. 6. A method according to any one of the preceding claims, wherein the still image frames are captured at a constant frame rate. 7. The method of any one of claims 1 to 6 , wherein capturing the still image frames comprises filming the object with a video camera. A device for measuring the coefficient of dynamic friction, comprising:
a memory for storing frames of still images arranged in chronological order of an object gliding on the surface;
an image recognizer that identifies the object in each of the frames;
a position calculation unit that analyzes an image of the identified object and calculates the position of the object for each frame;
a speed calculation unit that calculates the speed of the object from the time rate of change of the position of the object for each frame;
an acceleration calculation unit that calculates the acceleration of the object from the time rate of change of the speed;
a dynamic friction coefficient calculation unit that calculates a dynamic friction coefficient on the surface of the object based on acceleration of the object and gravitational acceleration;
with
The apparatus according to claim 1, wherein the acceleration calculator applies a least-squares method using a quadratic function to the time-series data of the speed of the object, and calculates the acceleration as a quadratic coefficient of the quadratic function. 9. The apparatus according to claim 8 , wherein said position calculator extracts regions of said object from each still image of said frame, and calculates positions of centers of gravity of said regions as positions of said object. 10. The apparatus according to claim 8 , wherein said image recognition unit recognizes features of said object and extracts a region of said object. 11. The apparatus of claim 10 , wherein the feature of the object is the color and/or shape of the object. 12. The apparatus according to any one of claims 8 to 11 , wherein the speed calculator calculates the speed of the object based on the ratio of the change in position of the object that occurs between frames to the time between frames. 13. Apparatus according to any one of claims 8 to 12 , wherein the still image frames are captured at a constant frame rate. 14. A method according to any one of claims 8 to 13 , wherein the frames of still images stored in the memory were generated sequentially by filming the object with a video camera. A program that causes an information processing device to execute the method for measuring the dynamic friction coefficient according to any one of claims 1 to 7 .

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