KR20180078736A - Apparatus and method for generating indoor map using duplication grid analysis - Google Patents

Abstract

According to the present invention, provided are an apparatus and a method to: convert a local map, measured about an environment of a large range of an area based on a range which a sensor is able to measure, into a local map grid; and generate an indoor map by using a part overlapped with a global map. The present invention comprises: a line extracting unit which extracts a line of an obstacle by converting data measured from a distance measurement sensor into coordinate data; a local map grid generating unit which generates a local map grid by generating a grid of the corresponding point based on a distance between the distance measurement sensor and a point within the line extracted from the line extracting unit; a redundant grid area extracting unit which extracts a grid mutually overlapped from a grid area of the generated local map grid and a previously stored global map grid; a robot position correcting unit which corrects a robot position according to the rotation and movement of a robot through a singular value decomposition (SVD) which is an SVD algorithm based on the redundant grid extracted from the redundant grid area extracting unit; and a global map updating unit which updates local map grid coordinates based on the robot position corrected in the robot position correcting unit and updates a grid based on the degree of the extracted redundant grid area, thereby updating an overall global map.

Description

[0001] The present invention relates to an indoor map generating apparatus and method using a redundant grid method,

The present invention relates to SLAM (Simultaneous Localization And Mapping) technology. The present invention relates to generation of a map of an environment and position measurement based on the generated map. In particular, To an apparatus and method for converting a measured local map into a local map grid and generating an indoor map using a portion overlapped with the global map.

In order for a robot to perform a given task, it is important to know the exact position of the robot. Among the many types of mobile robots, there is a method of generating a map on its own and measuring its position in the map in an environment where a landmark for a guidance line can not be installed.

When generating the map of the environment, the environment should be partially recognized based on the distance information that can be recognized by the sensor in the environment, and the map must be additionally connected and generated. Among these methods, there is SLAM (Simultaneous Localization And Mapping) technology. Among them, there is a method of solving a given problem based on grid by dividing a map into grid areas.

However, since the SLAM using the grid divides the map into a grid of a certain size, the memory usage is high and the calculation time is complicated. In particular, there is a problem that the environment takes a large amount of time in an environment having a large size and a large number of feature points such as a turning point. Therefore, a method for efficiently reducing the problem is needed.

Japanese Patent Application Laid-Open No. 10-2015-0115282 (published on October 10, 2015) Patent Registration No. 10-1503904 (Registration date 2015.03.12)

SUMMARY OF THE INVENTION The present invention has been conceived to solve the problems as described above, and it is an object of the present invention to provide a method and apparatus for converting a local map measured on the basis of a range measurable by a sensor into a local map grid, And to provide an apparatus and a method for generating an indoor map using the indoor map.

Other objects of the present invention are not limited to the above-mentioned objects, and other objects not mentioned can be clearly understood by those skilled in the art from the following description.

According to another aspect of the present invention, there is provided an indoor map generating apparatus using a redundant grid method, comprising: a line extracting unit for extracting a line of an obstacle by converting data measured by a distance measuring sensor into coordinate data; A local map grid generator for generating a grid of the point based on a distance between a point in the line extracted by the extractor and the distance measuring sensor to generate a local map grid, An overlapping grid area extracting unit for extracting a grid overlapping among the grid areas of the map grid based on the overlapping grid extracted by the overlapping grid area extracting unit, and a rotating unit for rotating and rotating the robot through singular value decomposition (SVD) A robot position correcting unit for correcting the robot position according to the movement, Update the local map grid coordinates based on the position correction in the robot unit, it is composed by including the extracted based on the degree of overlapping grid area update the grid to update global map to update the whole global map portion.

Preferably, the global map grid uses the stored global map grid if it is stored, and if not, stores the local map grid generated by the local map grid generator as a global map grid .

Preferably, the local map grid generator comprises: a point number calculating unit for calculating the number of points of all the extracted lines; a distance calculating unit for calculating a distance to the point in the extracted line from the distance measuring sensor; And a grid generating unit for generating a grid corresponding to a corresponding point in the grid size set by the grid size setting unit and adding the grid to the local map grid based on the grid size set by the grid size setting unit, .

Preferably, the grid size setting unit sets the grid size to be larger as the distance increases.

Preferably, the global map updating unit updates one grid with the size of the overlapping region when both the midpoints of the two grids are included in the overlapping region. If only one grid midpoint is included in the overlapping region, And the grid is updated to a region where the two grids are independent of each other when the center of gravity of the two grids is not included in the overlapping region.

According to another aspect of the present invention, there is provided a method of generating an indoor map using a redundant grid method, the method comprising: (A) calculating data of a position of a robot using kinematics, (B) converting the data measured from the distance measuring sensor through the line extracting unit into coordinate data and extracting a line of the measured obstacle, (C) calculating a distance between the point in the extracted line and the distance measuring sensor A step of generating a local map grid by generating a grid of corresponding points in a local map grid generating unit based on the local map grid generated by the local map grid generating unit, and (D) comparing the previously stored global map grid with the generated local map grid Extracting grids overlapping each other among the grid areas and storing them as pairs of corresponding points; and (E) Calculating a rotation value and a movement value of the robot using the singular value decomposition algorithm in the robot position correcting unit based on the lead and correcting the robot position based thereon; Updating the local map grid coordinates based on the extracted grid area, and updating the grid based on the extracted degree of the overlapped grid area to update the entire global map.

Preferably, the step (C) includes the steps of calculating the number of points of all the lines extracted through the point number calculating unit, and sequentially selecting the points calculated in the line one by one, Generating a grid corresponding to all points by setting a grid size according to a distance on the basis of the distance calculated through the grid size setting unit to generate a grid corresponding to all points; And generating the local map grid by adding the generated grid to the local map grid.

Preferably, the step (D) includes the steps of: selecting all the grids by sequentially generating the local map grids generated by the local map grid generating unit; selecting all the grids one by one by the global map grids; Extracting a grid overlapping among the global map grid and the local map grid area through comparison between the local map grid and the global map grid, and storing the extracted overlapping grids as pairs of corresponding points.

을 이용하여 산출하는 단계와, 상기 산출된 행렬 가중치를 기반으로 특이값 분해 알고리즘을 수행하여 로컬 맵 그리드의 대칭점 및 글로벌 맵 그리드의 대칭점을 행렬로 생성하는 단계와, 상기 생성된 행렬로 분해된 값을 이용하여 오류를 보정하기 위한 오류 가중치와 함께, 로봇의 회전값 및 이동값을 산출하여 로봇 위치를 보정하는 단계를 포함하여 이루어지는 것을 특징으로 한다.Preferably, the step (E) includes the steps of: detecting all local map grids and all global map grids of overlapping grids having pairs of corresponding points extracted by the overlapping grid region extraction unit; Calculating a symmetric point of each local map grid on the basis of the detected center point of the local map grid, calculating a center point of each global map grid based on the detected center point of the global map grid, (W) for eliminating an error occurring in a matrix for dividing the calculated point of symmetry of the local map grid and the singular point of the symmetric point of the global map grid,

Generating a symmetric point of the local map grid and a symmetric point of the global map grid by performing a singular value decomposition algorithm on the basis of the calculated matrix weight; And correcting the robot position by calculating a rotation value and a movement value of the robot together with an error weight for correcting the error by using the error weight.

Preferably, the step (F) includes the steps of: updating the local map grid coordinates based on the corrected robot position; selecting all the grids sequentially, one by one, and the global map grid sequentially Extracting a grid overlapping one of the regions of the selected local map grid and the global map grid; calculating a number of grids located in the overlapping region based on the degree of the overlapping region of the extracted grid; Updating the grid by setting an area based on the number of the calculated grids, and updating the global map using the updated grid.

Preferably, the number of grids is calculated by calculating the number of grids in which the midpoints of the grids are located in the overlapping regions of the grids.

Preferably, the step of updating the grid includes updating one grid to a size of the overlapping region when the number of generated ocpc is two or more, and if the number ocpc of the calculated ocpc is one A step of updating one grid with the size of an area including both grids, and a step of updating the grid with areas where the two grids are independent when the number of calculated grids (ocpc) is 0 .

As described above, the indoor map generating apparatus and method using the redundant grid technique according to the present invention have the following effects.

First, as a technique to overcome the problems of the grid-based SLAM technique, grids of different sizes are used, which can be viewed as a size indicating the uncertainty of the corresponding feature points, There is an effect that can be done.

Second, a wired / wireless type guidance system is required for guiding a mobile robot. However, when there is an environment in which the system can not be used according to the conditions of the environment, and the mobile robot can not be used due to disturbance of the surrounding environment, . For example, in a semiconductor factory or the like, it is impossible to use a wired / wireless type so that the robot must be guided to recognize the surrounding environment.

1 is a block diagram illustrating a configuration of an indoor map generating apparatus using a redundant grid technique according to an embodiment of the present invention;
FIG. 2 is a block diagram showing in detail the configuration of the local map grid generating unit in FIG.
3 is a flowchart illustrating a method of generating an indoor map using a redundant grid technique according to an embodiment of the present invention.
FIG. 4 is a flowchart illustrating a process of generating a local map grid in detail in FIG.
FIG. 5 is a block diagram illustrating in detail the process of generating a local map grid in FIG.
FIG. 6 is a flowchart for explaining a process of extracting a grid area overlapping a global map and a local map grid in FIG. 3
FIG. 7 is a flowchart for explaining a position correction process of the robot in FIG.
FIG. 8 is a flowchart for explaining updating of the global map in FIG.
FIG. 9 is a diagram for explaining updating of the global map in FIG.

Other objects, features and advantages of the present invention will become apparent from the detailed description of the embodiments with reference to the accompanying drawings.

A preferred embodiment of an indoor map generating apparatus and method using a redundant grid technique according to the present invention will be described with reference to the accompanying drawings. The present invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. It is provided to let you know. Therefore, the embodiments described in the present specification and the configurations shown in the drawings are merely the most preferred embodiments of the present invention and are not intended to represent all of the technical ideas of the present invention. Therefore, various equivalents It should be understood that water and variations may be present.

FIG. 1 is a block diagram illustrating a configuration of an indoor map generating apparatus using a redundant grid technique according to an embodiment of the present invention. Referring to FIG.

As shown in FIG. 1, the indoor map generating apparatus of the present invention includes a line extracting unit 100 for converting data measured from a distance measuring sensor into coordinate data and extracting a line of an obstacle, A local map grid generator 200 for generating a grid of the point based on the distance between the point in the line extracted by the distance map and the distance measuring sensor to generate a local map grid, An overlapping grid area extraction unit 400 for extracting a grid overlapping one of the grid areas of the local map grid based on the overlapping grid extracted by the overlapping grid area extraction unit 400, A robot position correcting unit 500 for correcting the robot position according to the rotation and the movement of the robot through the robot position correcting unit 500, Update the local map grid coordinates based on the position and the robot, is composed of the updated overlapping grid grid based on the degree of area determination to update the whole global map by updating the global map (600).

At this time, if the global map grid has been stored, the global map grid is used. If the global map grid is not stored, the local map grid generated by the local map grid generator 200 is used as a global map grid .

2, the local map grid generating unit 200 includes a point number calculating unit 210 for calculating the number of points of all the extracted lines, A grid size setting unit 230 for setting a grid size depending on the distance on the basis of the distance calculated by the distance calculating unit 220, And a grid generator 240 for generating a grid corresponding to the corresponding point with a grid size set in the grid 230 and adding the generated grid to the local map grid. At this time, the grid size setting unit 230 sets the grid size to be larger as the distance increases.

When the center of the two grids is included in the overlapping area, the global map updating unit 600 updates the overlapped area with one grid, and if there is only one grid center point in the overlapping area, In the case where any of the midpoints of the two grids is not included in the overlapping area, the two grids update the grid into independent areas.

The operation of the indoor map generating apparatus using the redundant grid method according to the present invention will now be described in detail with reference to the accompanying drawings. Like reference numerals in FIG. 1 or FIG. 2 denote the same members performing the same function.

3 is a flowchart illustrating a method of generating an indoor map using a redundant grid technique according to an embodiment of the present invention.

Referring to FIG. 3, when the measured data is obtained through the distance measuring sensor (S100), the position of the robot is calculated using the kinematics (S200). At this time, the distance measuring sensor generally measures about 0 ~ 80m, and thus it is possible to measure the distance to obstacles within 80m of the robot.

The data measured from the distance measuring sensor is converted into coordinate data through the line extracting unit 100 (S300), and the measured line of the obstacle is extracted (S400).

The local map grid generator 200 generates a grid of points based on the distance between the points in the extracted line and the distance measuring sensor to generate a local map grid (S500). The detailed method according to step S500 will be described below with reference to FIGS. 4 and 5. FIG.

If the existing global map is stored (S600), the global map grid is compared with the generated local map grid through the overlapping grid area extracting unit 400 to extract the overlapping grids among the grid areas and store them as pairs of corresponding points (S700). The detailed method according to the step S700 will be described below with reference to FIG. On the other hand, if the existing global map is not stored (S600), the generated local map grid is stored as a global map (S1000).

행렬에 대해 적용이 가능하다. 그리고 상기 S800 단계에 따른 상세한 방법은 아래에서 도 7을 참조하여 설명하도록 한다. Based on the superimposed grid having the pair of extracted points thus extracted, the robot position correcting unit 500 calculates the rotation value and the movement value of the robot using SVD (Singular Value Decomposition), which is a singular value decomposition algorithm, (S800). At this time, the SVD ignores the difficult conditions of eigenvalue decomposition,

It is applicable to matrix. The detailed method according to step S800 will be described below with reference to FIG.

Then, the local map grid coordinates are updated based on the corrected robot position through the global map updating unit 600, and the global map is updated based on the extracted degree of the overlapped grid area (S900) . The detailed method according to step S900 will be described below with reference to FIGS. 8 and 9. FIG.

In the case where the center of gravity of the two grids is included in the overlapping area, the update of the grid is updated to one grid in the size of the overlapping area. If only one grid center is included in the overlapping area, And if the overlapping region does not include any of the midpoints of the two grids, the two grids update the grid to be independent regions.

The detailed method according to step S500 will now be described.

FIG. 4 is a flowchart illustrating a process of generating a local map grid in FIG. 3, and FIG. 5 is a diagram illustrating a process of generating a local map grid in detail.

Referring to FIG. 4, the number of points (mps) of all lines extracted through the point number calculation unit 210 is calculated (S501). That is, as shown in Fig. 5 (a), the number of points constituting all the lines of the obstacle measured by the distance measuring sensor is calculated.

At this time, the points calculated in the line are sequentially selected one by one and the distances from the distance measuring sensor to each point (i) are calculated through the distance calculating unit 220 until all the points are selected (S502 to S503) ). The method of calculating the distance can be calculated using a formula (distance = speed * time) in which the distance increases in proportion to the time the laser emitted from the distance measuring sensor returns.

Then, the grid size according to the distance is set differently based on the distance calculated through the grid size setting unit 230 (S505), and a grid corresponding to all points (mps) is generated (S506). That is, as shown in FIG. 5 (b), the larger the distance between the distance measuring sensor and the obstacle, the larger the size of the generated grid.

Then, the grid generator 240 adds the generated grid to the local map grid to generate a local map grid as shown in FIG. 5C (S507).

The detailed method according to step S700 will be described below.

FIG. 6 is a flowchart illustrating a process of extracting a grid area overlapping a global map grid and a local map grid in FIG.

6, the local map grids generated by the local map grid generator 200 are sequentially selected one by one, all the grids lmc are selected (S701 to S703), and the global map grids are sequentially arranged one by one All the grids gmc select (S704 to S706) and compare them to extract a grid that overlaps the global map grid and the local map grid area (S707).

Then, the extracted overlapping grids are stored as pairs of corresponding points (S708).

The detailed method according to step S800 will be described below.

FIG. 7 is a flowchart for explaining the position correction process of the robot in FIG.

) 및 모든 글로벌 맵 그리드(

)를 검출한다(S801)(S802).Referring to FIG. 7, all the local map grids of the overlapping grid having the pair of corresponding points extracted by the overlapping grid area extracting unit 400

) And all global map grids (

(S801) (S802).

)의 중점(cp)과, 모든 글로벌 맵 그리드(

)의 중점(cx)을 검출한다(S803).And all detected local map grids (

(Cp) of all global map grids

(Step S803).

The symmetric point np of each local map grid is calculated based on the detected center point cp of the detected local map grid and the symmetric point nx of each global map grid is calculated based on the center point cx of the global map grid. (S804). The following equation (1) is a formula for calculating such a symmetry point (np) (nx).

Where p represents the local map grid, and x represents the global map grid. Cp represents the center point of the local map grid, and cx represents the center point of the global map grid.

As described above, the reason why the symmetry point of the grid is calculated is that when the mobile robot rotates, it must be rotated based on the origin, so that the accurate calculation is performed, so that the value of the symmetry point of the grid for changing the origin to zero is used.

The matrix weight W for eliminating an error generated in the matrix for dividing the calculated singular point of the symmetry point np of the local map grid and the symmetry point nx of the global map grid is calculated according to Equation (2).

행렬로 생성한다(S806).(http://tlaja.blog.me/220726154312 : 참조)Then, SVD (Singular Value Decomposition), which is a singular value decomposition algorithm, is performed based on the calculated matrix weights to calculate the symmetric point np of the local map grid and the symmetric point nx of the global map grid

(S806) (see http://tlaja.blog.me/220726154312: see)

Using the values thus decomposed into the matrices, the rotation value R and the movement value T of the robot together with the error weight W for correcting the error using the following equations (3), (4) And the position of the robot is corrected based on this calculation (S808) (S809).

직교 행렬을 나타내고, S는 대각 행렬을 나타내며, V는

직교 행렬을 나타낸다.At this time, U

S denotes a diagonal matrix, V denotes an orthogonal matrix,

Represents an orthogonal matrix.

The detailed method according to step S900 will be described below.

FIG. 8 is a flowchart for explaining updating of the global map in FIG. 3, and FIG. 9 is a diagram for explaining updating of the global map in FIG.

Referring to FIG. 8, the local map grid coordinates are updated based on the corrected robot position (S901).

9 (a), the local map grids sequentially select all grids lmc (S902 to S904), and the global map grids sequentially select all the grids gmc one by one (S904 to S907), and a grid overlapping among the global map grid (i) and the local map grid (j) region is extracted (S908).

Then, as shown in FIG. 9 (b), the number of grids (ocpc) located in the overlapping area is calculated based on the degree of the overlapped area of the extracted grid (S910) (S912). For example, in the case of two grids 10 and 20 positioned at the first position in FIG. 9 (b), the midpoints (A) and (B) of the two grids in the overlapping areas of the two grids 10 and 20 are all The number of grids to be calculated is two. In the case of the two grids 10 and 20 positioned at the second position, since only the midpoint B of one of the midpoints A and B of the two grids is located in the overlapping area of the two grids 10 and 20, The number of grids becomes 1. In addition, in the case of the two grids 10 and 20 located at the third position, since neither of the center points A and B of the two grids is located in the overlapping area of the two grids 10 and 20, Becomes zero.

If the number of calculated ocpc is two (S910), one grid is updated to the size of the overlapped region (S911). If the number of calculated ocpc is one (S912 ) One grid is updated to the size of the area including both grids (S913). If the number (ocpc) of the calculated grids is 0, the grid is updated to the independent regions of the two grids (S914). FIG. 9 (b) shows a grid that is updated according to the number of middle points (A) and (B) included in the overlapping area.

The global map updating unit 600 updates the global map using the grid thus updated.

While the present invention has been particularly shown and described with reference to exemplary embodiments thereof, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. It will be apparent to those skilled in the art that various modifications may be made without departing from the scope of the present invention. Accordingly, the true scope of the present invention should be determined by the technical idea of the appended claims.

Claims (12)

A line extracting unit for extracting a line of an obstacle by converting data measured from the distance measuring sensor into coordinate data,
A local map grid generator for generating a grid of points based on a distance between a point in the line extracted by the line extractor and the distance measuring sensor to generate a local map grid,
An overlapping grid area extracting unit for extracting a grid that is overlapped among a grid map area of the generated global map grid and a grid map area of the grid map area,
A robot position correcting unit for correcting the robot position according to the rotation and movement of the robot through SVD (Singular Value Decomposition) which is a singular value decomposition algorithm based on the overlapping grid extracted by the overlapping grid area extracting unit,
And a global map updating unit updating the local map grid coordinates based on the robot position corrected by the robot position correcting unit and updating the global global map based on the extracted degree of the overlapping grid area And generating an indoor map using the redundant grid method. The method according to claim 1,
When the global map grid has been stored, the global map grid is used. If the global map grid is not stored, the local map grid generated by the local map grid generating unit is stored as a global map grid and used An indoor map generation system using redundant grid technique. The apparatus of claim 1, wherein the local map grid generator
A point number calculating section for calculating the number of points of all extracted lines,
A distance calculating unit for calculating a distance from the distance measuring sensor to a point in the extracted line,
A grid size setting unit for setting a grid size depending on the distance based on the distance calculated by the distance calculating unit;
And a grid generating unit for generating a grid corresponding to the corresponding point with the grid size set by the grid size setting unit and adding the generated grid to the local map grid. The method of claim 3,
Wherein the grid size setting unit sets a larger grid size as the distance increases. The apparatus of claim 1, wherein the global map updating unit
In the case where the overlapping area includes all of the center points of two grids, the size of the overlapping area is updated to one grid. If only one grid center point is included in the overlapping area, And updating the grid to an independent region when the overlapping region does not include any one of the midpoints of the two grids. (A) a step of calculating the position of the robot using kinematics when measured data is obtained through the distance measuring sensor,
(B) converting data measured from the distance measuring sensor into coordinate data through a line extracting unit and extracting a line of the measured obstacle,
(C) generating a local map grid by generating a grid of corresponding points in a local map grid generator based on a distance between the point in the extracted line and the distance measuring sensor,
(D) comparing the generated global map grid with the global map grid stored in advance through the overlapping grid area extracting unit, extracting the overlapped grids among the grid areas and storing them as pairs of corresponding points,
(E) calculating a rotation value and a movement value of the robot using the singular value decomposition algorithm in the robot position correcting unit based on the overlapping grid having the extracted pair of corresponding points, and correcting the robot position based on the rotation value and the movement value,
(F) updating the local map grid coordinates based on the corrected robot position through the global map updating unit, and updating the grid based on the extracted degree of overlapping grid area to update the entire global map A method of generating an indoor map using a redundant grid technique. 7. The method of claim 6, wherein step (C)
Calculating a number of points of all lines extracted through the point number calculating unit,
Selecting one of the points calculated in the line one by one and calculating the distance to the distance measuring sensor and each point through the distance calculating unit until all the points are selected;
Generating a grid corresponding to all the points by setting a grid size according to the distance based on the distance calculated through the grid size setting unit;
And generating a local map grid by adding the generated grid to a local map grid through a grid generating unit. 7. The method of claim 6, wherein step (D)
Selecting all the grids by sequentially generating the local map grids generated by the local map grid generating unit one by one,
Selecting all the grids by sequentially performing global map grids one by one,
Extracting a grid overlapping among the global map grid and the local map grid region by comparing the selected local map grid and the global map grid,
And storing the extracted overlapping grids as a pair of corresponding points. 7. The method of claim 6, wherein step (E)
Detecting all local map grids and all global map grids of overlapping grids having corresponding pairs extracted from the overlapping grid region extracting unit,
Detecting a midpoint of all the detected local map grids and a midpoint of all global map grids,
Calculating symmetric points of each local map grid based on the detected center point of the local map grid,
Calculating symmetric points of each global map grid based on the detected center point of the global map grid,
The matrix weight W for eliminating errors generated in the matrix for dividing the calculated point of symmetry of the local map grid and the singular point of the symmetric point of the global map grid is expressed by the following equation

; And
Performing a singular value decomposition algorithm based on the calculated matrix weights to generate a matrix of symmetry points of the local map grid and a global map grid;
And correcting the robot position by calculating a rotation value and a movement value of the robot together with an error weight for correcting the error using the value decomposed by the generated matrix. How to create an indoor map. 7. The method of claim 6, wherein step (F)
Updating the local map grid coordinates based on the corrected robot position,
Selecting all the grids sequentially, one by one,
The global map grid sequentially selecting all the grids one by one,
Extracting a grid overlapping one of the regions of the selected local map grid and the global map grid;
Calculating a number of grids located in overlapping areas based on the degree of overlapping areas of the extracted grids;
Updating the grid by setting an area based on the number of the calculated grids;
And updating the global map by using the updated grid. 11. The method of claim 10,
Wherein the number of grids is calculated by calculating the number of grids in which the center of each grid is located in a region where the grids overlap. 11. The method of claim 10, wherein updating the grid comprises:
Updating one grid to a size of an overlapped area when the number of calculated grids (ocpc) is two or more,
Updating one grid to a size of an area including both grids when the number of calculated grids (ocpc) is one,
And updating the grid to an area in which the two grids are independent when the number of calculated ocpc is zero (0).

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