KR102521915B1 - Method and apparatus of detecting transparent obstacles using laser range finder - Google Patents

Abstract

A transparent obstacle recognition method using a laser distance finder of the present invention includes the steps of determining whether a measured distance using a beam of the laser distance finder is in an effective range; Obtaining the absolute position coordinates of the obstacle using the measured distance and the current position; obtaining a grid number in which the obstacle is measured on the absolute position coordinates; determining whether the grid number obtained from the previous beam and the measured grid number match; determining whether the robot including the laser distance meter is in a stationary state when the grid number obtained from the previous beam and the measured grid number do not match; When the robot is stopped, determining whether the possibility of an obstacle of the grid corresponding to the grid number is higher than an opaque obstacle threshold; and determining a transparent obstacle based on the probability of the obstacle if the obstacle is not higher than the opaque obstacle threshold.

Description

Transparent obstacle recognition method and apparatus using laser distance meter {METHOD AND APPARATUS OF DETECTING TRANSPARENT OBSTACLES USING LASER RANGE FINDER}

The present invention relates to a method and apparatus for recognizing a transparent obstacle using a laser range finder, and more particularly, to a method for recognizing a transparent obstacle using only a laser range finder used by a mobile robot to prevent a collision while driving.

Recently, various mobile robots used indoors, mainly cleaning robots and service robots, have been developed and commercialized. Mobile robots must avoid obstacles while driving, and for this, it is essential to recognize the surrounding environment. Various sensors are being used for the recognition of the surrounding environment, and among them, the most commonly used sensor for mobile robots is the laser distance meter. A laser distance meter uses a laser to detect obstacles in a certain area.

However, recently, various materials have been used for the interior. Among them, the use of transparent obstacles such as glass or plastic materials is also increasing. Such a transparent obstacle has a disadvantage in that it is difficult to detect using only a laser distance measurer due to the nature of the material. As a result, a double burden occurs, such as attaching a separate sensor for detecting transparent obstacles to the mobile robot.

Accordingly, an object of the present invention is to propose a method for recognizing a transparent obstacle using only a laser distance measurer in a traveling mobile robot.

An object of the present invention is to provide a method for a mobile robot to detect a transparent obstacle while moving using only a laser distance meter in an environment including a transparent obstacle.

In order to achieve the above object, the present invention provides a method for recognizing a transparent obstacle using a laser distance finder comprising the steps of determining whether a measured distance using a beam of a laser distance finder is in an effective range; Obtaining the absolute position coordinates of the obstacle using the measured distance and the current position; obtaining a grid number in which the obstacle is measured on the absolute position coordinates; determining whether the grid number obtained from the previous beam and the measured grid number match; determining whether the robot including the laser distance meter is in a stationary state when the grid number obtained from the previous beam and the measured grid number do not match; When the robot is stopped, determining whether the possibility of an obstacle of the grid corresponding to the grid number is higher than an opaque obstacle threshold; and determining a transparent obstacle based on the probability of the obstacle when the value is not higher than the opaque obstacle threshold.

According to another aspect of the present invention, a transparent obstacle recognition device includes a laser distance finder; And it is determined whether the measured distance using the beam of the laser distance finder is in an effective range, the absolute position coordinates of the obstacle are obtained using the measured distance and the current position, and the grid number at which the obstacle is measured is obtained on the absolute position coordinates, It is determined whether the grid number obtained from the previous beam and the measured grid number match, and if the grid number obtained from the previous beam and the measured grid number do not match, it is determined whether the robot including the laser distance meter is in a stationary state. And, when the robot is stopped, determining whether the obstacle possibility of the grid corresponding to the grid number is higher than the opaque obstacle threshold value, and if not higher than the opaque obstacle threshold value, determining a transparent obstacle based on the obstacle possibility obstacle judge

include

According to an embodiment of the present invention, by using a method of accumulating reflection noise generated when attempting to detect a transparent obstacle in laser distance measurement (LRF), a mobile robot without a separate sensor other than a laser rangefinder It enables autonomous driving without colliding with transparent obstacles.

1 is a block diagram of a transparent obstacle recognizing apparatus according to an embodiment of the present invention;
Figure 2 is a view visually showing the meaning of the nth beam of the laser distance measurement (LRF) in Figure 1;
Figure 3 is a diagram showing the relationship between the coordinate system of the robot and laser distance measurement (LRF) according to an embodiment of the present invention.
FIG. 4 is a diagram showing numbers of grids including obstacles measured by an n-th beam in FIG. 1;
5 is a diagram showing a final grid map in an environment including transparent obstacles according to an embodiment of the present invention.
6 is a diagram showing an overall flowchart for generating a grid map in an environment with transparent obstacles according to an embodiment of the present invention.
7 to 8 are diagrams showing a flow chart for determining transparent obstacles through the possibility of obstacles in the grid of FIG. 6;

Since the present invention can make various changes and have various embodiments, specific embodiments are illustrated in the drawings and will be described in detail through detailed description. However, this is not intended to limit the present invention to specific embodiments, and should be understood to include all modifications, equivalents, and substitutes included in the spirit and scope of the present invention. In describing the present invention, if it is determined that a detailed description of related known technologies may unnecessarily obscure the subject matter of the present invention, the detailed description will be omitted. Also, as used in this specification and claims, the terms "a" and "an" are generally to be construed to mean "one or more" unless stated otherwise.

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. do it with

The present invention is a method and apparatus for detecting a transparent obstacle by using reflection noise generated by a beam of the LRF when a robot sensing its surroundings through an LRF encounters a transparent obstacle during autonomous navigation. At this time, the robot is based on a grid map method for autonomous driving.

1 is a block diagram of a transparent obstacle recognizing device according to an embodiment of the present invention.

Referring to FIG. 1 , the robot including the transparent obstacle recognizing device 100 may include a Laser Range Finder (LRF) 110 and an obstacle determination unit 120.

The robot may measure the distance to the obstacle using the beam of the laser distance measurer 110 .

Referring to FIG. 2 , the laser distance meter 110 of the robot may output a plurality of beams to determine an obstacle. The maximum number of beams of the laser distance meter 110 varies depending on the unique resolution and implantation range of the laser distance meter 110 . The length of the red line shown in FIG. 2 indicates the maximum recognition range (effective range) of the laser distance meter 110, and this also depends on the performance of the laser distance meter 110.

The laser distance meter 110 outputs n (constant) beams at the current point in time t. At this time, the n-th beam means a beam number emitted to the LRF. The minimum and maximum values of the range of n vary according to the performance (resolution, detection range) of the laser distance meter 110 and the reference point.

The laser distance measuring device 110 may measure distances for all output beams. A method of measuring the distance of the laser distance measurer 110 will be described in detail with reference to FIG. 6 below.

The obstacle determining unit 120 may determine whether the measured distance is within an effective range for the performance of the laser distance measuring device. At this time, if the obstacle determination unit 120 is within the effective range, it can obtain the absolute position coordinates of the obstacle through the measured current position of the robot, the measured distance, and the direction using Equation 1.

Here, Equation 1 will be described with reference to FIG. 3 .

Figure 3 is a diagram showing the relationship between the coordinate system of the robot and the laser distance measurement (LRF) according to an embodiment of the present invention.

The red circle in FIG. 3 represents a robot, xrobot and yrobot are the center point position of the robot, d is the measured distance using the beam, xlrf and ylrf are the absolute position coordinates of the obstacle, and are the direction of movement of the robot and the direction of the beam, respectively. The angle of , can indicate the moving direction of the robot.

Referring back to FIG. 1 , the obstacle determination unit 120 obtains the absolute position coordinates of the obstacle using Equation 1, and then obtains the grid number including the coordinates on the grid map.

At this time, the obstacle determining unit 120 may assign a meaningless grid number if the measurement distance does not belong to the effective range of the laser distance measuring device 110 .

A method for the obstacle determining unit 120 to obtain a grid number including an obstacle measured by the n-th beam of the laser distance meter 110 will be described with reference to FIG. 4 .

FIG. 4 is a diagram showing numbers of grids including obstacles measured by the n-th beam in FIG. 1 .

As shown in FIG. 4, the obstacle determining unit 120 is a lattice of lattices with obstacles measured by the n-th beam and the n-1th beam of the LRF output from the laser distance finder 110. number can be obtained. Depending on the embodiment, the grid number is 25, and the obstacle may be located at the second grid number.

Referring back to FIG. 1, the obstacle determination unit 120 calculates the grid number for the n-th beam and compares it with the grid number for the immediately preceding n-1-th beam, and if the two grid numbers are the same, the grid number corresponding to the grid number It can increase the possibility of obstacle inclusion.

The obstacle determination unit 120 may determine whether the robot is stationary when the two grid numbers do not match.

The obstacle determination unit 120 does not update the final grid map (map) if the robot is stationary. In this case, the final grid map is a map used by the robot during autonomous driving. At this time, the reason why the final grid map is not updated is that even when the robot is stationary, the laser distance meter 110 is continuously operating, and then reflection noise is continuously accumulated to create an incorrect map.

If the robot continues to move without stopping, the obstacle determination unit 120 may determine whether the possibility of an obstacle of the grid corresponding to the grid number is high enough to determine an opaque obstacle.

The obstacle determination unit 120 may update the grid obstacle possibility to the final grid map if the grid obstacle possibility is sufficiently high.

The obstacle determination unit 120 may determine a transparent obstacle when the possibility of an obstacle in the grid is not high enough to screen out an opaque obstacle. A method of determining a transparent obstacle will be described in detail with reference to FIGS. 7 and 8 below.

The obstacle determination unit 120 determines that the grid corresponding to the obtained grid number is not sufficiently likely to be an obstacle (possibility of being an opaque obstacle is low), but is greater than or equal to a certain value (more than the possibility of a transparent obstacle) or at time t-1 (previous time) It can be determined whether there is a matching grid among the grids that have been measured.

The obstacle determination unit 120 may determine whether the obstacle possibility of the grid corresponding to the grid number is 0 at time t (current time) if at least one of the obstacle possibility is sufficiently high and a predetermined value or more is not satisfied. .

If the probability is 0, the obstacle determination unit 120 may increase the probability of an obstacle of the grid corresponding to the grid number to a minimum size and update the final grid map.

The obstacle determination unit 120 may make the obstacle possibility of the corresponding mustard to 0 when the obstacle possibility of the grid corresponding to the grid number is not 0.

On the other hand, the obstacle determination unit 120 may calculate the grid where the robot is located when any one of the case where the possibility of the obstacle is sufficiently high and the case where the obstacle is greater than or equal to a predetermined value is satisfied.

The obstacle determination unit 120 draws a virtual line segment between the grid where the robot is located and the grid corresponding to the grid number, creates a grid set having all grids passing through the line segment as elements, and creates a grid closest to the position of the robot in the grid set. can bring

The obstacle determination unit 120 may determine whether the nearest grid has a possibility of being an obstacle even a little on the final grid map.

If there is no possibility that the obstacle is an obstacle, the obstacle determining unit 120 may delete the nearest lattice from the lattice set and create a new lattice set with the remaining lattices.

The obstacle determination unit 120 may determine whether there are remaining grids in the grid set, and if there are remaining grids, the process of selecting the grid closest to the position of the robot from the remaining grid sets may be repeated.

The obstacle determination unit 120 may determine that the nearest grid has a possibility of an obstacle in the final grid map.

The obstacle determination unit 120 may determine whether the obstacle of the grid corresponding to the grid number is likely to be a transparent obstacle.

The obstacle determination unit 120 may sufficiently increase the possibility of an obstacle of the nearest grid when there is a possibility of a transparent obstacle, and increase the possibility to a minimum level when there is no possibility, and then update the final grid map. In this process, when the robot moves in close proximity to the surface of the transparent obstacle and determines the position of the obstacle using the beam of the laser distance meter 110, the noise with a repetitive pattern generated when the beam collides with the transparent obstacle is used to determine the transparent obstacle. This may be a process that increases the possibility of obstacles in the grid where it is located.

The obstacle determining unit 120 obtains a partial grid set excluding the closest grid from the grid set, and then distinguishes a grid closest to the position of the robot from among the grids of the partial grid set.

The obstacle determining unit 120 may determine whether a grid corresponding to a grid number exists in the partial grid set and whether the grid is likely to be a transparent obstacle.

If there is no possibility of a transparent obstacle, the obstacle determining unit 120 may reduce the possibility of an obstacle of a grid closest to the position of the robot among the partial grid sets to the minimum.

If there is a possibility that the obstacle is a transparent obstacle, the obstacle determiner 120 may update the final grid map with the result after sufficiently lowering the possibility of the obstacle of the grid closest to the position of the robot among the partial grid set. This process may be a process of reducing the possibility of obstacles in the grids that are determined to be obstacles despite the grids having no obstacles due to noise generated from grids other than the grids where the transparent obstacles are located.

The obstacle determination unit 120 may exclude a lattice closest to the robot from the partial lattice set and obtain a new partial lattice set using the remaining elements. Thereafter, the obstacle determination unit 120 repeats until no element of the sublattice set remains.

If no elements of the partial grid set remain, the obstacle determining unit 120 may determine whether there are remaining grids in the original grid set and repeat the entire process.

If there is no grid remaining in the grid set, the obstacle determination unit 120 determines whether the probability of all grids in the grid set being obstacles on the final grid map is 0, and if all grids are 0, the probability of obstacles of the grid corresponding to the grid number is minimized, After updating the grid map, the process of Figure 2 can be completed.

5 is a diagram showing a final grid map in an environment including transparent obstacles according to an embodiment of the present invention.

Referring to FIG. 5 , it is a result generated by applying an environment map generation algorithm in an environment in which obstacles of the obstacle detection unit are transparent. At this time, black represents a cell with a high probability of having an obstacle, and the closer the cell is to white, the lower the probability of having an obstacle in the grid.

As a result, it was found that the robot detecting the transparent obstacle excludes the place where the robot starts. However, some of the cells left as obstacle candidates can be judged on the other side of the transparent obstacle because the algorithm cannot remove all the reflection noise.

6 is a diagram showing an overall flowchart for generating a grid map in an environment with transparent obstacles according to an embodiment of the present invention.

In step S101, the obstacle determination unit 120 may measure the distance to the obstacle using the N-th beam of the LRF at time t through the laser distance measurer 110.

In step S102, it may be determined whether the measurement distance of the n-th beam is in an effective range.

In step S102, if the measurement distance of the n-th beam is not within the effective range, in step S103, n times? It can indicate that there are no grid numbers that contain obstacles measured by the beam.

When the measured distance of the n-th beam in step S102 is within the effective range, the absolute position coordinates of the obstacle can be obtained using the distance measured in step S104 and the current position of the robot.

In step S105, a grid number including an obstacle measured by the n-th beam on the grid map can be obtained using the absolute position coordinates.

After step S103 or step S105, it may be determined whether the grid number obtained for the n-1th beam in step S106 matches the grid number using the nth beam.

If the grid numbers match in step S106, the possibility that the grid corresponding to the grid number includes the obstacle can be increased in step S107.

If the grid numbers do not match in step S106, it can be determined whether the robot is stopped in step S108.

When the robot is stopped in step S108, the final grid map update may not be performed in step S109.

If the robot does not stop in step S108, it may be determined in step S110 whether the probability of an obstacle of the grid corresponding to the grid number is higher than the opaque obstacle threshold.

If the probability is higher than the opaque obstacle threshold in step S110, a final grid map update may be performed in step S111.

In step S110, if the probability is not higher than the opaque obstacle threshold value, transparent obstacle determination may be performed through the obstacle possibility in step S112.

After any one of steps S107, S109, S111, and S112, it may be determined whether all LRF beams are used at time t in step S113. That is, it can be determined whether the size of n is maximum.

When beams of all LRFs are used in step S113, the robot may move based on the final grid map in step S114.

Meanwhile, when beams of all LRFs are not used in step S113, step S101 may be performed again.

7 to 8 are diagrams showing a flow chart for determining transparent obstacles through the possibility of obstacles in the grid according to an embodiment of the present invention.

Referring to FIGS. 7 and 8 , in step 201, the obstacle determination unit 120 uses the absolute position coordinates to determine whether the obstacle possibility of the grid corresponding to the grid number on the grid map is higher than the transparent obstacle candidate threshold or t- It can be determined whether there is a matching grid among the grids measured at one point in time.

If there is no matching grid in step 201, in step S202, the obstacle determination unit 120 may determine whether the obstacle possibility of the grid corresponding to the grid number at time t is zero.

If the possibility is 0 in step S202, in step 203, the obstacle determining unit 120 may increase the possibility of an obstacle of the grid by a specified size.

In step S204, the obstacle determination unit 120 may perform a final grid map update.

On the other hand, if the possibility is not 0 in S202, the obstacle determination unit 120 may make the obstacle possibility of the grid 0.

In addition, if there is a matching lattice in step 201, in step S206, the obstacle determination unit 120 may calculate the position of the lattice including the current center of the robot.

In step S207, the obstacle determining unit 120 may draw a virtual line segment between the lattice where the center of the robot is located and the lattice corresponding to the lattice number, and create a lattice set through which the line segment passes.

In step S210, the obstacle determination unit 120 may bring a grid closest to the position of the robot from the grid set.

In step S211, the obstacle determination unit 120 may determine whether the probability that the grid closest to the position of the robot is an obstacle on the final grid map is greater than 0.

If the probability is not greater than 0 in step S211, in step S212, the obstacle determination unit 120 may erase the grid closest to the position of the robot from the grid set and create a new grid set with the remaining grids.

In step S213, the obstacle determination unit 120 may determine whether there are remaining grids in the grid set.

In step S213, if there are remaining grids in the grid set, the obstacle determining unit 120 may perform step S210.

In addition, when there are no grids remaining in the grid set in step S213, the obstacle determining unit 120 may determine whether the possibility that all grids in the grid set are obstacles on the final grid map is zero in step S214.

In step S214, if the probability of being an obstacle is 0, in step S215, the obstacle determining unit 120 may increase the possibility of an obstacle of a grid corresponding to a grid number by a specified size and update the final grid map.

Meanwhile, if the probability is greater than 0 in step S211, in step S220, the obstacle determining unit 120 may determine whether the obstacle of the grid corresponding to the grid number is equal to or greater than the transparent obstacle surface threshold.

In step S220, if it is equal to or greater than the obstacle surface threshold value, in step S221, the obstacle determining unit 120 may increase the possibility of an obstacle of the grid closest to the position of the robot by a weight.

In addition, if it is not greater than or equal to the obstacle surface threshold value in S220, in step S222, the obstacle determining unit 120 may increase the possibility of an obstacle of the grid closest to the position of the robot by a designated value and a designated size.

After step S221 or step S222, in step S223, the obstacle determining unit 120 may perform a final grid map update.

In step S224, the obstacle determination unit 120 may exclude a grid closest to the robot from the grid set and obtain a partial grid set including the remaining grids.

In step S225, the obstacle determining unit 120 may obtain a grid closest to the position of the robot next among the partial grid sets.

In step S226, the obstacle determination unit 120 may determine whether the obstacle of the grid corresponding to the grid number is equal to or greater than the transparent obstacle surface threshold.

If it is equal to or greater than the transparent obstacle surface threshold value in step S226, in step S227 the obstacle determination unit 120 may lower the possibility of an obstacle of the grid closest to the position of the robot by a weight.

If it is not equal to or greater than the transparent obstacle surface threshold value in step S226, in step S228, the obstacle determining unit 120 may lower the possibility of an obstacle in a lattice closest to the position of the robot among the partial lattice sets by a specified value.

After step S227 or step S228, in step S230, the obstacle determination unit 120 may perform a final grid map update.

In step S231, the obstacle determination unit 120 may obtain a partial grid set including the remaining grids after excluding the grid closest to the robot from the remaining partial grid sets.

In step S232, the obstacle determination unit 120 may determine whether elements of the sublattice set remain.

If elements of the sublattice set remain in step S232, the obstacle determination unit 120 may perform step S225.

In step S232, when no elements of the partial grid set remain, the obstacle determining unit 120 may perform step S213.

The above-described age estimation method may be implemented as computer readable code on a computer readable medium. The computer-readable recording medium may be, for example, a removable recording medium (CD, DVD, Blu-ray disc, USB storage device, removable hard disk) or a fixed recording medium (ROM, RAM, computer-equipped hard disk). can The computer program recorded on the computer-readable recording medium may be transmitted to another computing device through a network such as the Internet, installed in the other computing device, and thus used in the other computing device.

In the above, even though all the components constituting the embodiment of the present invention have been described as being combined or operated as one, the present invention is not necessarily limited to these embodiments. That is, within the scope of the object of the present invention, all of the components may be selectively combined with one or more to operate.

Although actions are shown in a particular order in the drawings, it should not be understood that the actions must be performed in the specific order shown or in a sequential order, or that all shown actions must be performed to obtain a desired result. In certain circumstances, multitasking and parallel processing may be advantageous. Moreover, the separation of the various components in the embodiments described above should not be understood as requiring such separation, and the described program components and systems may generally be integrated together into a single software product or packaged into multiple software products. It should be understood that there is

So far, the present invention has been looked at mainly by its embodiments. Those skilled in the art to which the present invention pertains will be able to understand that the present invention can be implemented in a modified form without departing from the essential characteristics of the present invention. Therefore, the disclosed embodiments should be considered from a descriptive point of view rather than a limiting point of view. The scope of the present invention is shown in the claims rather than the foregoing description, and all differences within the equivalent scope will be construed as being included in the present invention.

Claims (11)

Determining whether the measured distance using the beam of the laser distance meter is an effective range;
Obtaining the absolute position coordinates of the obstacle using the measured distance and the current position;
obtaining a grid number in which the obstacle is measured on the absolute position coordinates;
determining whether the grid number obtained from the previous beam and the measured grid number match;
determining whether the robot including the laser distance meter is in a stationary state when the grid number obtained from the previous beam and the measured grid number do not match;
When the robot is stopped, determining whether the possibility of an obstacle of the grid corresponding to the grid number is higher than an opaque obstacle threshold; and
If not higher than the opaque obstacle threshold, determining a transparent obstacle based on the possibility of the obstacle
A transparent obstacle recognition method using a laser distance meter.
According to claim 1,
When the grid number obtained from the previous beam and the measured grid number match, comparing the grids indicated by the beams of the current step and the beams of the previous step to increase the possibility that the grid contains an obstacle
A transparent obstacle recognition method using a laser distance meter.
According to claim 1,
If higher than the opaque obstacle threshold, performing a final grid map update.
A transparent obstacle recognition method using a laser distance meter.
According to claim 1,
The step of determining the transparent obstacle is
creating a lattice set using a lattice corresponding to the current position of the robot and the lattice number at which the obstacle is measured;
increasing the possibility of obstacles in the lattice set where the transparent obstacles are located in the lattice set; and
performing a final grid map update based on the increased obstacle probability.
A transparent obstacle recognition method using a laser distance meter.
According to claim 4,
After the final grid map update is performed, reducing the possibility of obstacles in a grid other than the grid where the transparent obstacle is located; and
Further comprising performing a final grid map update based on the lowered obstacle probability.
A transparent obstacle recognition method using a laser distance meter.
laser distance meter; and
It is determined whether the measured distance using the beam of the laser distance meter is in an effective range, the absolute position coordinates of the obstacle are obtained using the measured distance and the current position, the grid number at which the obstacle is measured is obtained on the absolute position coordinates, and the previous It is determined whether the grid number obtained from the beam and the measured grid number match, and if the grid number obtained from the previous beam and the measured grid number do not match, it is determined whether the robot including the laser distance meter is in a stationary state, , When the robot is stopped, it is determined whether the obstacle possibility of the grid corresponding to the grid number is higher than the opaque obstacle threshold value, and if it is not higher than the opaque obstacle threshold value, an obstacle that determines a transparent obstacle based on the obstacle possibility including the judge
Transparent obstacle recognition device.
According to claim 6,
The obstacle determination unit
When the grid number obtained from the previous beam and the measured grid number match, comparing the grid pointed by the beam of the current step and the beam of the previous step to increase the possibility that the grid contains an obstacle
Transparent obstacle recognition device.
According to claim 6,
The obstacle determination unit
If the opacity is higher than the obstacle threshold, a final grid map update is performed.
Transparent obstacle recognition device.
According to claim 6,
The obstacle determination unit
Create a lattice set using the lattice corresponding to the current position of the robot and the lattice number where the obstacle is measured
In the lattice set, the possibility of obstacles in the lattice where the transparent obstacle is located is increased,
Final grid map update based on increased obstacle probabilities.
Transparent obstacle recognition device.
According to claim 9,
The obstacle determination unit
After the final grid map update, reduce the possibility of obstacles on grids other than the grid where the transparent obstacle is located,
Final grid map update based on lowered obstacle probabilities.
Transparent obstacle recognition device.
A computer program that executes any one of the transparent obstacle recognition methods of claims 1 to 5 and is recorded on a computer-readable recording medium.

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