CN111737882A

CN111737882A - Method for selecting landing area for realizing autonomous obstacle avoidance in complex lunar surface approach segment

Info

Publication number: CN111737882A
Application number: CN202010707586.0A
Authority: CN
Inventors: 吴鹏; 穆荣军; 邓雁鹏; 刘丽丽
Original assignee: Harbin Institute of Technology
Current assignee: Harbin Institute of Technology
Priority date: 2020-07-21
Filing date: 2020-07-21
Publication date: 2020-10-02
Anticipated expiration: 2040-07-21
Also published as: CN111737882B

Abstract

A method for selecting a landing area for realizing autonomous obstacle avoidance at a complex lunar surface approaching segment solves the problem that the information utilization rate is not high enough when autonomous obstacle avoidance and landing area selection are carried out in the conventional lunar soft landing, and belongs to the technical field of lunar soft landing. The method comprises the following steps: s1, acquiring an optical image of the lunar surface measured at the approaching segment, and determining a landing zone to be selected; s2, extracting shape information of a ring-shaped mountain in the landing zone to be selected, reconstructing the ring-shaped mountain in the landing zone to be selected by combining Fractal Brownian Motion (FBM), calculating the gradient of each point in the ring-shaped mountain, and obtaining an area with the gradient smaller than the safety gradient as a landing zone according to the set safety gradient; s3, performing texture analysis on the landing zone to be selected, and evaluating roughness to obtain a flat plot of the landing zone to be selected; and S4, combining the landing areas capable of being lowered and the flat land blocks to select the optimal feasible landing areas. The method provided by the invention can accurately reflect the shape characteristics of the circular mountains and the lunar surface in the lunar surface image, can effectively select the area suitable for landing, and has good engineering adaptability.

Description

Method for selecting landing area for realizing autonomous obstacle avoidance in complex lunar surface approach segment

Technical Field

The invention relates to a method for selecting a landing area for realizing autonomous obstacle avoidance in a complex lunar surface approach section, and belongs to the technical field of soft landing of a moon.

Background

Since the 60 s of the 20 th century, several lunar probes were launched in the united states, soviet union, europe, japan, china, india, and other countries and regions. For an early lunar exploration task, due to the lack of autonomous obstacle avoidance capability, a wide and flat place is usually planned as a task landing area before the task is implemented, such as a Luna series detector and an explorationist series detector; or the obstacle avoidance function is realized by means of manual operation, such as Apollo series detectors. In order to improve the landing success rate, the lunar probe is required to have the capability of automatically selecting a landing point.

Since 21 st century, the united states proposed an unmanned smart landing autonomous soft landing obstacle avoidance technique based on lidar, but based on the existing data, the technique has not been successfully applied. In the soft landing tasks of the 'ChangE' three-model and the 'ChangE' four-model aircrafts, a rough and precise combined obstacle avoidance algorithm is adopted to carry out autonomous obstacle avoidance and landing area selection. The method mainly comprises the steps of performing 'rough obstacle avoidance' in an approaching section (2400m-100m), resetting a guidance target and planning a landing area on the basis of optical information obtained by passive detection; in the hovering, obstacle avoidance and slow descending sections (100m-2m), lunar surface high-precision terrain information is obtained by adopting sensors such as a laser radar, a laser altimeter and the like, and an optimal landing point is selected to realize 'fine obstacle avoidance'.

The difficulty of the technology for avoiding the autonomous obstacle of the soft landing of the moon and selecting the landing area is that information of a lunar surface high-precision Elevation map (DEM) is lacked before a task is executed, and a detector cannot finish larger obstacle avoidance maneuver when obtaining more accurate lunar surface Elevation information at the tail stage of the landing. At present, based on passive optical detection information obtained by a close section, obstacle identification and safe landing area selection are mainly realized by analyzing light and shade gray scale characteristics of obstacles such as annular mountains and stones, and the information utilization rate is not high enough.

Disclosure of Invention

Aiming at the problem that the information utilization rate is not high enough when the conventional autonomous obstacle avoidance and landing area selection are carried out on lunar soft landing, the invention provides a landing area selection method for realizing autonomous obstacle avoidance on a complex lunar near segment, which carries out rough reconstruction on a near segment to be selected on the basis of fully analyzing the shape characteristics of a lunar ring mountain, recovers three-dimensional information from a two-dimensional image and improves the information utilization rate.

The invention discloses a method for selecting a landing area for realizing autonomous obstacle avoidance in a complex lunar access segment, which comprises the following steps:

s1, acquiring an optical image of the lunar surface measured at the approaching segment, and determining a landing zone to be selected;

s2, extracting shape information of a ring-shaped mountain in the landing zone to be selected, reconstructing the ring-shaped mountain in the landing zone to be selected by combining Fractal Brownian Motion (FBM), calculating the gradient of each point in the ring-shaped mountain, and obtaining an area with the gradient smaller than the safety gradient as a landing zone according to the set safety gradient;

s3, performing texture analysis on the landing zone to be selected, and evaluating roughness to obtain a flat plot of the landing zone to be selected;

and S4, combining the landing areas capable of being lowered and the flat land blocks to select the optimal feasible landing areas.

Preferably, the S2 includes:

s21, extracting the annular mountain of the landing area to be selected, performing circle fitting, and calculating the inter-pit-lip diameter D of the fitted annular mountain;

s22, obtaining the depth H of the annular mountain and the height H of the pit lip according to the first formula and the second formula_r：

H＝0.196D^1.01Formula one

H_r＝0.036D^1.014Formula two

S23, according to the diameter D between the pit lips, the depth H and the height H of the pit lips of the annular mountain_rObtaining the equivalent radius D of the outer edge of the lip of the pit_r：

S24, approximating the circular mountain to a spherical surface, and calculating the equivalent spherical radius R of the circular mountain:

s25, according to the diameter D, the depth H and the height H of the inter-pit lip of the annular mountain_rOuter edge equivalent radius of pit lip D_rDetermining the shape of the circular mountain by the equivalent spherical radius R, and superposing the circular mountain by applying the FBM based on fractal Brownian motion to form a circular mountain simulation point;

s26, calculating the gradient psi of each point in the circular mountain according to the simulation points of the circular mountain;

s27, according to the set safety gradient psi^*And obtaining an area with the gradient smaller than the safety gradient as a landing area.

Preferably, the safety gradient psi^*＝12。

Preferably, in S3:

s31, dividing the lunar surface optical image of the landing zone to be selected into lunar surface image textures of N categories according to different gray features, wherein the gray features are used for representing the features of a flat land block;

and S32, performing texture analysis on each type of lunar surface image texture in the to-be-selected landing area by using a K-means clustering method to obtain a clustering result, and determining a flat plot according to the clustering result.

Preferably, N is 6, and 6 categories are respectively a flat lunar surface, a rough lunar surface, a large toroidal mountain vulva surface, a large toroidal mountain sunny surface, a small toroidal mountain vulva surface and a small toroidal mountain sunny surface.

The invention has the beneficial effects that: aiming at a gray image obtained by optical detection of a detector, firstly modeling annular mountain shape characteristics and distribution characteristics obtained by detection, and calculating the gradient of each point in a landing zone to be selected; then, evaluating the roughness of the landing area to be selected by adopting an image texture analysis method based on K-means clustering; the method comprehensively considers the gradient and the roughness, and selects the feasible landing area in the landing area to be selected, and has the following three specific advantages: (1) the utilization rate of passive optical detection information is improved, and the autonomous navigation and obstacle recognition precision is improved; (2) the obstacle structure of the invisible area can be restored, and the autonomy of the lunar probe in selecting the landing area is obviously improved; (3) more accurate and reliable initial information is provided for the 'ChangE' series detector fine obstacle avoidance system. Simulation experiments are carried out, and the experiments show that the method provided by the invention can accurately reflect the shape characteristics of the hills and the lunar surface in the lunar surface image, can effectively select the area suitable for landing, and has good engineering adaptability.

Drawings

FIG. 1 is a schematic flow diagram of the present invention;

FIG. 2 is a circular mountain extraction and circle fitting;

FIG. 3 is an equivalent cross-sectional view of a ring mountain;

FIG. 4 is a three-dimensional shape fitting of a hill of toroid;

FIG. 5 is a simulated point cloud of a ring mountain;

FIG. 6 is a sample image of Chang E;

FIG. 7 is an equivalent slope of each point in the ring hill;

FIG. 8 shows texture analysis results;

FIG. 9 is a profile value distribution;

FIG. 10 is a result of different class number profile values;

FIG. 11 is a flat lunar surface texture after the expansion process;

FIG. 12 is an image taken by the "Chang E" detector;

FIG. 13 is a candidate landing area zone (zone A);

FIG. 14 is a fractal Brownian motion slope estimation;

FIG. 15 shows the feasible landing area selection result (area A);

FIG. 16 is a landing zone to be selected (zone B);

FIG. 17 shows the feasible landing area selection result (area C).

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict.

The invention is further described with reference to the following drawings and specific examples, which are not intended to be limiting.

In the moon soft landing task, autonomous navigation and obstacle avoidance are carried out simultaneously, and the method mainly comprises the key technologies of autonomous navigation, obstacle identification and landing point selection, obstacle relative navigation, obstacle avoidance guidance and control and the like. In the embodiment, the ChangE series aircraft is taken as an example, and the ChangE series detector is arranged behind the attitude adjusting section, and the optical camera approximately vertically points to the lunar surface from the height of the approaching section of 1500m, so that the landed area to be selected is observed, the terrain obstacle information is acquired, and the rough obstacle avoidance is carried out. And after the ChangE' third detector reaches 100m of the hovering section, detecting a landing area in 30s by adopting sensors such as a laser radar and a laser speedometer, selecting a safe landing point and mechanically descending to 30m above the landing point to finish the precise obstacle avoidance work of the obstacle avoidance section. The landing time sequence of the 'ChangE' fourth detector is basically the same as that of the 'ChangE' third detector, but the 'ChangE' third detector completes the landing task under the guidance of the ultrahigh-resolution image acquired by the 'ChangE' second detector, and the 'ChangE' fourth detector completes the landing task under the condition of no imaging reference, so that the landing environment is complicated and changeable, the configured sensor has longer acting distance and the approaching section approximately vertically falls. Landing obstacle avoidance timing sequence as

Shown in table 1.

TABLE 1 landing obstacle avoidance sequence

The embodiment aims at the selection of a feasible landing area of a close section, and comprises the following steps:

acquiring an optical image of the surface of the moon measured in an approaching section, and determining a landing area to be selected according to flight mission planning; in the first step, preprocessing such as denoising and binarization needs to be carried out on the lunar surface optical image, so that extraction of the ring mountains and lunar surface texture analysis are facilitated.

Extracting shape information of the ring-shaped mountain in the landing zone to be selected, reconstructing the ring-shaped mountain in the landing zone to be selected by combining Fractal Brownian Motion (FBM), calculating the gradient of each point in the ring-shaped mountain, and obtaining an area with the gradient smaller than the safety gradient according to a set safety gradient to serve as a landing zone;

thirdly, performing texture analysis on the landing area to be selected, and evaluating the roughness of the landing area to be selected to obtain a flat plot of the landing area to be selected;

and step four, selecting the optimal feasible landing area by combining the landing area capable of being lowered and the flat land parcel.

The present embodiment also provides an explanation about the lunar reconstruction based on FBM:

the lunar surface natural terrain conforms to the two-dimensional FBM characteristic and is a Gaussian random process, and a corresponding random variable X is obeyed to N (0, t)^α) and (3) random distribution, wherein alpha is a dimension and represents the roughness, and the lunar surface terrain statistics self-similarity, variation difference and section power spectral density respectively satisfy the following formulas (1) to (3).

p(X(t)<x)＝p(X(γt)<γ^Ht) (1)

E[X(t+h)-X(t)]²＝k|h|^2H(2)

G(ω)＝2πkω^-H(3)

In the formula: gamma is the number of iterative layers, k is the scale factor, and H is the irregular dimension. Fractal dimension F_DHas a relationship with H^[17]：

F_D+H＝3.

When the lunar surface is simulated by using the FBM, H (H is more than or equal to 0 and less than or equal to 1) is calculated by using a first-order absolute moment estimation method.

In the formula (4) B_H(t) is FBM function, and is obtained by taking logarithm of formula (4)

Equation (5) approximates a linear relationship.

Two-dimensional FBM function B for lunar surface_H(u) let u be (u)_x,u_y) A point position vector of the form:

in the formula:

ω (x, y) is two-dimensional white gaussian noise. And reconstructing the lunar terrain DEM data by the ' Chang ' E ' second three-dimensional image to calculate the lunar surface dimension.

Firstly, a lunar surface two-dimensional FBM function B is calculated_H(u) mean of the increments in both directions:

wherein N is the selected NxN data window width, and delta is the incremental calculation step length, and 50m is taken. Calculating an overall average value:

taking logarithm of the above formula according to formula (5) to obtain:

log(E(Δ))＝log(E_Const)+(3-F_D)log(Δ) (10)

it can be derived that:

calculating fractal dimension F in any 5 image regions of 200 × 200 in existing data_DThe results are as follows:

TABLE 2 lunar fractal dimension

Numbering	1	2	3	4	5
						Irregular dimension	0.762	0.284	0.466	0.559	0.961
Fractal dimension	2.238	2.716	2.534	2.441	2.039

The fractal dimension of the selected five regions is larger than 2, which shows that the lunar fractal property is good, and FBM can be adopted for reconstruction. And (4) superposing lunar surface annular mountain information on the basis of the FBM reconstruction to finish terrain simulation.

In a preferred embodiment, the second step of the present embodiment includes:

step two, extracting a circular mountain of the landing area to be selected for circle fitting, and calculating the diameter D between pit lips of the fitted circular mountain, as shown in FIG. 2;

step two, acquiring the depth H of the annular mountain and the height H of the pit lip according to the formulas (12) and (13)_r：

H＝0.196D^1.01(12)

H_r＝0.036D^1.014(13)

The distribution quantity rule of the ring mountains on the lunar surface can be represented by the following statistical model:

lgN(D)＝b×lg(D)+lg(a) (14)

in the formula: d represents the diameter of the circular mountain, N (D) is the number of the circular mountains with the diameter larger than D in the unit area, and a and b are model parameters. The statistical distribution parameters of different sizes of the hills in the moon and the moon are given, as shown in table 3 (unit: meter).

TABLE 3 annular mountain fractal distribution parameters

According to statistics, the number of meteorite craters on the surface of the moon is more than 33000, and the relation between the height and the diameter of the lunar surface annular mountain conforms to the empirical formulas (12) and (13).

Step two and step three, the section view of the annular mountain is shown in figure 3, according to the diameter D between the pit lips, the depth H and the height H of the pit lips of the annular mountain_rObtaining the equivalent radius D of the outer edge of the lip of the pit_r：

Step two, approximating the annular mountain to a spherical surface, and calculating the equivalent spherical radius R of the annular mountain according to the formulas (12) and (13):

the result of the circular hill shape fitting is shown in fig. 4;

step two and step five, according to the diameter D, the depth H and the height H of the pit lip between the pit lips of the annular mountain_rOuter edge equivalent radius of pit lip D_rDetermining the shape of the circular mountain by the equivalent spherical radius R, and superposing the circular mountain by applying the FBM based on fractal Brownian motion to form a circular mountain simulation point; on the basis of fig. 4, the FBM is applied to superpose the ring mountains to form a ring mountain simulation point cloud picture as shown in fig. 5.

Step two, calculating the gradient psi of each point in the ring-shaped mountain according to the simulation points of the ring-shaped mountain:

in the formula: (x)₀,y₀) The circle center is detected for the annular mountain, and the (x, y) are coordinates of each point in the annular mountain.

Step two and seven, according to the set safety gradient psi^*And obtaining an area with the gradient smaller than the safety gradient as a landing area.

The embodiment sets the safe gradient psi of the coarse obstacle avoidance feasible landing zone^*12. The closer to the edge of the annular mountain, the greater the terrain gradient, so that the obstacle avoidance gradient threshold psi is selected^*Thereafter, the corresponding feasible landing zone and feasible landing zone radius d within the annular mountain may be determined, as shown in FIGS. 6(a) - (d).

d＝Rsin(ψ^*) (13)

In FIG. 6(a), D is the diameter between the lips of the annular mountain pit, D_rIs the equivalent radius of the outer edge of the lip of the annular mountain pit; the depth H of the circular hill and the equivalent spherical radius R of the circular hill can be calculated by the equations (12) and (16), as shown in fig. 6 (c); after the annular mountain is fitted, the gradient of each point in the annular mountain can be calculated by the formula (12), as shown in fig. 6 (d); by selecting a safety gradient psi^*A landable area in the current parcel may be obtained, as shown in fig. 6 (b).

The landing zone can be lowered to only meet the requirement of the landing zone for landing gradient, and the roughness of the land parcel needs to be considered simultaneously for selecting a feasible landing zone, in a preferred embodiment, the third step of the implementation method comprises the following steps:

step three, dividing the lunar surface optical image of the landing zone to be selected into lunar surface image textures of N categories according to different gray features, wherein the gray features are used for representing the features of a flat land block;

and step two, performing texture analysis on each type of lunar surface image texture in the to-be-selected landing zone by using a K-means clustering method to obtain a clustering result, and determining a flat plot according to the clustering result.

The K-means clustering algorithm is an unsupervised classification algorithm and can be used for carrying out texture analysis on a lunar optical detection image. The texture analysis has the functions of evaluating the roughness of the landing area to be selected, selecting a relatively flat land parcel, and taking the area with smaller gradient and very flat as a feasible landing area, thereby improving the reliability of autonomous obstacle avoidance and soft landing.

In a preferred embodiment, N is 6, and 6 categories are flat lunar surface, rough lunar surface, large toroidal mountain vulva surface, large toroidal mountain sunny surface, small toroidal mountain vulva surface, and small toroidal mountain sunny surface, respectively.

There are 6 kinds of labeled data clusters Ci (i ═ 1,2, …,6), as shown in table 4. And (3) performing texture analysis by applying a K-means clustering algorithm. The image gray matrix is set as a label-free data set, and n points exist.

X＝[x⁽¹⁾x⁽²⁾... x⁽ⁿ⁾]^T(14)

C＝[C₁,C₂,C₃,C₄,C₅,C₆](15)

TABLE 4 lunar surface image texture Classification

Dividing the images into 6 clusters according to the classification number K-6, and constructing a minimization loss objective function J:

in the formula: mu.s_iIs a cluster C_iA center point of (a); non-viable cells|xⁱ-μ_i||²Is a cluster C_iThe distance between each point in the graph and the center point.

And selecting a lunar surface image sample shot by the detector Chang E I for texture analysis, wherein the image sample is shown as a graph in FIG. 7.

The K-means cluster texture analysis was performed on FIG. 7, and the analysis results are shown in FIG. 8.

Fig. 8(a) to (f) show the same region, and the corresponding white region in the land parcel is the selected land parcel that meets the condition. FIG. 8(a) the white area is a smaller annular mountain shade surface; FIG. 8(b) the white area is a larger annular mountain shade surface; FIG. 8(c) the white area is a rough lunar surface; FIG. 8(d) the white area is a flat moon surface; FIG. 8(e) the white area is a smaller circular mountain sunny side; fig. 8(f) the white area is the larger annular mountain sunny side.

After the clustering result is obtained, the clustering result is evaluated by using an outline Coefficient S (Silhouette Coefficient). For any point i in the grayscale image: the intra-cluster dissimilarity a (i) represents the degree of cohesion of the cluster, and a (i) is the average value of the distances from i to other points in the same cluster; the inter-cluster dissimilarity b (i) represents the degree of separation of the cluster, and b (i) is the minimum value of the distance from i to the center of the other clusters. The i-point contour coefficient S (i) is:

the contour coefficient S of the cluster is:

the closer S is to 1, the better the clustering result is, the higher the degree of aggregation of the data clusters is, and the more dispersed the different data clusters are; when S (i) <0, the point clustering is not reasonable, and the point clustering is divided into other data clusters. The clustering results of fig. 7 and 8 are evaluated, fig. 7 is divided into 4 to 7 categories, and the profile value distribution is calculated, and the result is shown in fig. 9.

When the cluster category number is 6, the number of gray sample points with negative contour values is the minimum, which shows that the cluster data cluster separation degree is good and the cluster separation degree is high when the cluster data are classified into 6 types.

The number of different classes corresponding to the contour values is shown in fig. 10.

Considering the integrity of the ring mountains in the lunar surface texture analysis, when the clustering category is 8, the segmentation is excessive, the region where the same ring mountain is located is easily segmented into a plurality of two parts, and the complete ring mountain is not easy to identify; when the number of partitions is too small, the target terrain meeting the landing conditions cannot be extracted, so that 4-7 clustering numbers can be selected, and the corresponding clustering contour values and the clustering duration are shown in table 5:

TABLE 5 Cluster Profile and Cluster Length

When the clustering number is 6, the clustering contour value is the largest, which shows that the proposed lunar surface image texture analysis based on K-means clustering can classify lunar surface gray level images according to task requirements, distinguish actual terrains corresponding to different image textures, and provide support for selecting feasible landing areas.

And (d) selecting the flat lunar surface corresponding to the texture in the figure 8 as a feasible landing area according to the texture analysis result of the lunar surface image. Fig. 11(a) is the original image of the flat lunar surface of fig. 8(d), and the white area in the original image is expanded to form fig. 11(b), wherein the roughness of the white area in fig. 11(b) is small, so that all the circular mountains are basically avoided and the landing can be realized.

And (3) experimental verification:

the lunar surface image shot by the detector "Chang E" I is selected as an analysis sample, and feasible landing areas are selected based on fractal features and lunar surface texture analysis respectively as shown in FIG. 12 (a).

First, the original image is subjected to gaussian blurring and binarization processing, and the annular mountain edge and diameter in the image are identified, as shown in fig. 12 (b).

According to the mission planning requirement, a certain area (area A) is arbitrarily selected as a landing area to be selected on FIG. 12(a), as shown in FIG. 13.

Reconstructing the terrain of the figure 13 through the FBM and calculating the terrain slope of each point; the slope of the safe landing zone is set to 12 deg., and the land mass with a slope greater than the safe slope is obtained as shown in the black area of fig. 14.

In FIG. 14, the black blocks are areas with larger average slopes and cannot be used as feasible landing areas. Meanwhile, texture analysis is performed on fig. 13, the landing feasibility evaluation is performed by comprehensively considering the gradient and the roughness of the image area, and a feasible landing area is selected as shown in fig. 15:

another landing zone to be selected (zone B) in fig. 12 is taken for analysis, as shown in fig. 16 (a); the evaluation of landing feasibility is performed to obtain a feasible landing area as shown in fig. 16 (b):

in fig. 16, a feasible landing zone is selected by comprehensively considering the results of the image texture analysis and the FBM estimated gradient, and a "black" flat area is located in the upper left corner but not selected as a feasible landing zone because the area is located inside a circular mountain and the gradient is large.

In fig. 12, an area (C area) with uneven image gray value distribution is selected and evaluated for landing feasibility, and a feasible landing area cannot be obtained, as shown in fig. 17.

It can be seen that, aiming at different landing areas to be selected, the method can reconstruct the terrain, identify obstacles and autonomously select effective feasible landing areas on the basis of reconstructing the lunar surface.

Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that features described in different dependent claims and herein may be combined in ways different from those described in the original claims. It is also to be understood that features described in connection with individual embodiments may be used in other described embodiments.

Claims

1. The method for selecting the landing area for realizing autonomous obstacle avoidance in the complex lunar surface approach segment is characterized by comprising the following steps of:

2. The method for selecting a landing zone for obstacle avoidance in a complex lunar access segment as claimed in claim 1, wherein said S2 comprises:

H＝0.196D^1.01Formula one

H_r＝0.036D^1.014Formula two

3. The method for selecting a landing zone for avoiding an autonomous obstacle in a complex lunar access segment as claimed in claim 1, wherein the safety gradient ψ is^*＝12。

4. The method for selecting a landing zone for obstacle avoidance in a complex lunar access segment as claimed in claim 1, wherein in said S3:

5. The method for selecting a landing zone for achieving autonomous obstacle avoidance in a complex lunar surface approaching segment as claimed in claim 4, wherein said N is 6, and 6 categories are respectively a flat lunar surface, a rough lunar surface, a large annular mountain cloudy surface, a small annular mountain cloudy surface and a small annular mountain cloudy surface.