China Chang′e 4 Probe

High‐Resolution Terrain Analysis for Lander Safety Landing and Rover Path Planning Based on Lunar Reconnaissance Orbiter Narrow Angle Camera Images: A Case Study of China's Chang'e‐4 Probe Bo Li1,2,3 , Zongyu Yue2 , Jiang Zhang1, Xiaohui Fu1 , Zongcheng Ling1 , Shengbo Chen3, Jian Chen1 , and Peiwen Yao1

1Shandong Provincial Key Laboratory of Optical Astronomy and Solar‐Terrestrial Environment; Institute of Space Sciences, Shandong University, Weihai, China, 2State Key Laboratory of Remote Sensing Science, Institute of Remote Sensing and Digital Earth, Chinese Academy of Sciences, Beijing, China, 3College of Geoexploration Science and Technology, Jilin University, Changchun, China

Abstract China's Chang'e‐4 (CE‐4) probe will explore the South Pole‐Aitken basin in late 2018. Its preselected landing area is located on the southeastern floor of the Von Kármán crater. Landing experience of China's Chang'e‐3 probe may not be applied to CE‐4 mission directly because the topography of lunar farside is more rugged. Moreover, due to scale dependence and smooth effects, the previous topographic studies derived from digital elevation model data with lower resolution cannot represent the meter‐scale topographic features. Because of low time and space complexities in lunar images, image segmentation algorithm is especially suitable for recognizing lunar features. We divided the narrow angle camera (NAC) mosaic image into three parts: dark area, bright area, and flat area, based on a double‐threshold Otsu method. The first two parts corresponded to the undulating areas (positive and negative terrains). And then we calculated the flat area percentage (Fap) of the previous successful lunar landing missions (including Chang'e‐3, Apollo, Surveyor, and Luna series) and obtained the Fap threshold (>0.6) for lunar safe landing. According to Fap map (~1.5 m per pixel) of CE‐4 preselected landing area, the divided square grids with a size of 0.01° can be classified into safe grids (Fap > 0.6) and unsafe grids (Fap ≤ 0.6). The CE‐4 preselected landing areas can be greatly reduced to five potential landing areas. In the last, we proposed a route planning method, which took both the distance and security into account, for CE‐4 rover to dynamically generate a safe and short route between current grid and target grid.

Plain Language Summary China's Chang'e‐4 (CE‐4) probe will land on the South Pole‐Aitken basin at the end of 2018. Its preselected landing area (45–46°S, 176.4–178.8°E) is located on the southeastern floor of the Von Kármán crater. It is a very large area, and there are many small (meter‐scale) topographic features such as rocks, craters, ridges, and troughs. Therefore, it is necessary to narrow the scope and choose the safe landing areas from the preselected landing area. The flat area percentage (Fap) is an important factor to measure the safety of landing area. Based on an image segmentation method, we extracted Faps in square grids with a size of 0.01°and then the CE‐4 landing areas were reduced to five safe areas. After CE‐4 lands at the safe site, a rover will be released to travel around. We proposed a path planning method for CE‐4 rover moving from current grid to target grid. This method took both the distance and security into account to find out the best path with safety and short distance.

1. Introduction

Since the Luna‐1 mission in 1959, there have been many successful lunar explorations by orbiters and land- ers, such as Luna, Surveyor, Apollo, and Chang'e missions. However, the early lunar landing sites were restricted to the midlatitudes because of technological limitations. Today, the recent lunar missions (such as Chang'e‐4 [CE‐4] and Luna‐25) are interested in the lunar subpolar areas (±65–85° latitudes; Kokhanov et al., 2017; Ye et al., 2017).

Luna‐25 is designed for launching and landing on a lunar subpolar area in 2019. The objective of Luna‐25 is to explore the lunar polar resources and the lunar exosphere to study the content of polar water ice. For

©2019. The Authors. This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distri- bution in any medium, provided the original work is properly cited, the use is non‐commercial and no modifica- tions or adaptations are made.

RESEARCH ARTICLE 10.1029/2018EA000507

Key Points: • NAC mosaic image was divided into

three parts with a resolution of ~1.5 m using a double‐threshold Otsu method

• The range of CE‐4 preselected landing area was greatly reduced to five potential landing areas according to the flat area percentage

• A route planning method was proposed to dynamically generate a safe and short route between current grid and target grid for CE‐4 rover

Supporting Information: • Supporting Information S1

Correspondence to: B. Li and S. Chen, [email protected]; [email protected]

Citation: Li, B., Yue, Z., Zhang, J., Fu, X., Ling, Z., Chen, S., et al. (2019). High‐resolution terrain analysis for lander safety landing and rover path planning based on Lunar Reconnaissance Orbiter Narrow Angle Camera images: A case study of China's Chang'e‐4 probe. Earth and Space Science, 6, 398–410. https://doi.org/ 10.1029/2018EA000507

Received 22 OCT 2018 Accepted 29 JAN 2019 Accepted article online 4 FEB 2019 Published online 12 MAR 2019

LI ET AL. 398

Luna‐25, 12 potential landing sites (PLSs) were selected according to several criteria. For example, surface slopes at the landing site must be less than 7° at a baseline of 2.5 m, and the illumination level within the landing area must be more 40% over the day, and so on (Mitrofanov et al., 2016). And then a topographical and photogeological study of three PLSs (1, 4, and 6) was carried out to characterize their safety conditions and possible sources of materials (Ivanov et al., 2018). And the hilly unit in PLS 6 is among the safest terrains for the Luna‐25 landing.

China's CE‐4, the first in situ exploration of lunar farside, will explore the South Pole‐Aitken basin in late 2018 (Wu et al., 2017). The preselected landing area (45–46°S, 176.4–178.8°E) for CE‐4 is located on the southeastern floor of the Von Kármán crater (Figure 1a). The diameter of Von Kármán crater is ~186 km, and its central coordinates is 44.4°S, 176.2°E. Von Kármán crater is a degraded pre‐Nectarian impact crater, flooded with mare basalts in its floor. CE‐4 will choose a safe landing site to land, which is orbited by a rover to execute some geologic investigation tasks. China's Chang'e‐3 (CE‐3) lunar probe has successfully landed on a young lava plain in northern Mare Imbrium, in December 2013. And Yutu rover explored the lunar sur- face targets and subsurface near a young crater using its main scientific instruments (Di et al., 2016; Ling et al., 2015; Xiao et al., 2015). But the successful experience of CE‐3 landing and roving may not be applied to CE‐4 mission directly, because the topographies of lunar farside are more rugged and difficult for the safe landing and traversing objective. (1) The preselected landing region for CE‐4 is older than the landing site of CE‐3 mission. The landing area of CE‐3 can be divided into two basaltic units, and the absolute model ages of these two units are ~3.17 and ~3.48 Ga (Li, Ling, et al., 2016). Based on different TiO2 contents of basaltic units, Ling et al. (2018) classified the mare region on Von Kármán crater's floor into two units, whose abso- lute model ages were ~3.70 (Haruyama et al., 2009) and ~3.65 Ga. Therefore, the CE‐4 preselected landing area has more large impact craters and a higher crater density than CE‐3 landing site. Large craters within a landing site represent potential hazards to landers as well as navigational threats to rovers. (2) There are more small geomorphic features such as degraded secondary crater chains, sinuous ridges, and troughs (Figure 1b) in CE‐4 preselected landing area than the CE‐3 landing site. These ridges are asymmetric in shape and extend in a sinusoidal‐like shape, whose widths are tens of meters (Huang et al., 2018). While sin- uous troughs are formed between the ridges, both the troughs and ridges are concentrated in the west of the landing region.

For early lunar landing missions (such as Luna and Surveyor series), lunar probes did not have obstacle iden- tification and avoidance capabilities due to limited techniques at that time. While in Apollo missions, the success rate of safe landing was improved because the astronauts observed the landing area and manipulated the control system to avoid the obstacles (Sears, 1964). In the future unmanned Martian and lunar landing missions, the autonomous obstacle‐avoiding technology using laser imaging radar is proposed (Johnson et al., 2002; Wong & Singh, 2002). When the probe drops to a certain height, the lunar surface is scanned by laser imaging radar. Obstacles are identified based on the slope and roughness maps derived from the three‐dimensional DEM data. But this new technology has not been achieved and applied. Several studies have analyzed the terrains and landforms of the CE‐4 and CE‐5 preselected landing area based on digital

Figure 1. (a) Lunar Reconnaissance Orbiter wide angle camera mosaic of Von Kármán crater. The white box shows the Chang'e‐4 (CE‐4) preselected landing area. (b) The troughs (yellow arrows) in the floor of Von Kármán crater.

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elevation model (DEM) data. For example, Wu et al. (2015) proposed an autonomous hazard detection and rough‐fine hazard avoidance guidance method for soft lunar landing. This method mitigates the landing risks due to the uncertainty and hazards of the lunar terrain, such as surface roughness and slope. Huang et al. (2018) thought that the proposed CE‐4 landing area was usually flat, based on the fact that almost 99% of the area has a slope less than 15° and 94% of the area has a slope less than 5° at a ~59‐m scale length. Zhao et al. (2017) found that Rümker plateau (a candidate landing site for the CE‐5 mission) stands 200–1,300 m above the surrounding mare surface and 75% of the plateau has a slope of less than 3° at a base- line length of ~30 m. However, these results were not suitable for guiding CE‐4 landing and rover route plan- ning. Because these topographic analyses were performed based on the merged DEM and the resolutions of the produced slope map was ~59‐ and ~30‐m scale. According to the previous studies, the lunar topographic textures (such as slope, roughness, and entropy values) show scale dependence (Cao et al., 2015; Kreslavsky et al., 2013; Li et al., 2015; Li, Wang, et al., 2016; Robbins, 2018). Kreslavsky et al. (2013) found that hectometer‐scale lunar roughness poorly correlated with kilometer‐scale lunar roughness, because they reflected different sets of geologic processes and time scales. Li, Wang, et al. (2016) used the statistical moments of gray level histograms in different‐sized neighborhoods (e.g., 3, 5, 10, 20, 40, and 80 pixels) to compute the kilometer‐scale roughness and entropy values based on a WAC mosaic image. They found that large roughness and entropy signatures were only shown in larger‐scale maps, while the smallest three‐pixel scale map had more disorderly and unsystematic textures. Perhaps, there is a smooth effect in the process of generating larger‐scale textures. In this process smaller textures resulting from tiny topographical and com- positional changes may be removed. Thus, the resolutions of the slope maps derived from the DEM data with ~59‐ and ~30‐m scale are not high enough to represent the smaller topographic features (such as rocks, ridges, and troughs) with a meter scale.

In this paper, we used Lunar Reconnaissance Orbiter (LRO) narrow angle camera (NAC) images with a deci- meter resolution to (1) divide NACs covering the CE‐4 preselected landing site into three parts: dark area, bright area, and flat area, based on an image segmentation algorithm. The first two parts correspond to the undulating area (positive and negative terrains, PNTs) of the lunar surface. (2) Calculate the flat area per- centage (Fap) of the previous successful lunar landing missions (including CE‐3, Apollo, Surveyor and Luna series) and obtain the Fap threshold for lunar safety landing. (3) Classify the CE‐4 preselected landing area into regular grids and evaluate the safety of each grid to choose potential landing areas (PLAs). (4) Traverse out all the paths between the current grid and target grid of CE‐4 rover to find out the best path with safety and short distance.

2. NAC Image Segmentation Using a Double‐Threshold Otsu Method 2.1. LRO NAC Images

LRO was launched on 18 June 2009 and entered lunar orbit on 23 June 2009. The LRO Camera consists of two NACs with about 50 cm per pixel resolution from an altitude of 50 km (Robinson et al., 2010). LRO is an exploration mission with a primary goal of identifying desirable safe landing sites on the Moon. The LRO NAC images provide information on the distribution of craters and slopes over small baselines, with the technique of shadowed‐area analysis (Abdrakhimov et al., 2015). Here we selected 27 single NAC images to cover the CE‐4 preselected landing area. The details of these NAC images were listed in the Table 1. As far as possible, the NAC images with the incidence angles between 60° and 80° were selected to ensure that the image contrast is large, and the PNTs are obvious in these images. In order to ensure the accuracy of Fap measurements, Lambert Conformal Conic Projection was used to reduce the projective deformation. This projection is based on the GCS_MOON_2000 (a geographic coordinate system) whose datum is the D_Moon_2000 in GIS software. In this projection coordinate system, all NAC images were registered and then mosaiced into one image with a resolution ~1.5 m per pixel (Figure 2a), but with some small residual gaps (white areas marked by yellow arrows in Figure 2a).

2.2. Double‐Threshold Otsu Method

Lunar and Martian landers are sensitive to PNTs (including rocks, craters, ridges, troughs, and secondary crater chains). PNTs can lead lander to tilt or tip over with remaining horizontal velocity, impact the under- side and damage the lander, and can prevent complete opening of the solar arrays after landing (Golombek et al., 2012). In addition, when the rover patrols, the area below the rover must be free of PNTs likely

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damaging the rover's lower structure. Therefore, PNTs on the surface of a planet represent an obvious hazard to landing spacecraft and a potential impediment to traveling. The more exactly PNTs on a land- ing site can be recognized, the better the potential hazards to the lander and rover can be described and avoided. Identifying the PNTs at PLSs through remote sensing data is thus critical for the suc- cess of landing tasks.

On lunar and other planetary surfaces, shadows and bright areas in remote sensing images or in situ photographs are caused by the pre- sence of raised or depressed features, which are interpreted as PNTs, that is, uneven areas (Golombek et al., 2008). However, the bright- ness changes on lunar images may also be caused by different compo- nent distributions. Von Kármán crater is a degraded pre‐Nectarian impact crater, flooded with mare basalts on its floor. Due to long‐ term and continuous impact events from the pre‐Nectarian period to the present, the regolith covering Von Kármán crater's floor was fully mixed. Thus, we thought that the brightness changes on lunar images caused by compositional difference were subtle and even neg- ligible. Several studies have applied this criterion to identify indivi- dual rocks on lunar and Martian surfaces using remote sensing or in situ images (Cintala & Mcbride, 1995; Di et al., 2016; Li et al., 2017; Liasis & Stavrou, 2016; Wang et al., 2017).

Each PNT consists of two parts (dark and bright areas) in lunar images under the sunlight. Here we used an image segmentation algorithm to identify PNTs and extract flat areas on CE‐4 preselected landing area based on the mosaic NAC image. (1) Nowadays, there is almost no internal geological process and few external impact pro- cesses on the Moon. Compared with the weathering on Earth, the only space weathering process on the Moon is too weak to modify

the lunar surface morphology. The topographic and structural features on lunar surface almost do not vary with time at present. Therefore, lunar remote sensing images have much lower time complexity than Earth remote sensing images. (2) Compared with the abundant activities on Earth, there is no production, life and modification activity caused by human, animals, and plants on the Moon. And the ground objects are rich in color, shape, and texture on Earth, while there are only monochrome and simple objects on the Moon. Therefore, lunar remote sensing images have much lower space complexity than Earth remote sensing images. Because of low complexity in time and space of lunar images, image segmentation algorithm is espe- cially suitable for recognizing and extracting lunar features.

Otsu's method (Otsu, 1979) is optimum in the sense that it maximizes the between‐class variance, a well‐ known measure used in statistical discriminant analysis (Gonzalez & Woods, 2007). The basic idea is that well‐thresholded classes should be distinct with respect to the intensity values of their pixels and, conversely, that a threshold giving the best separation between classes in terms of their intensity values would be the best (optimum) threshold. The Otsu method can be extended to an arbitrary number of thresholds, because the separability measure on which it is based also extends to an arbitrary number of classes (Fukunaga, 1990). In this paper, the NAC images were classified into three parts, which were dark areas, bright areas, and flat areas. Therefore, we focused attention on image segmentation using two optimum thresholds.

Let {0, 1, 2, ..., L‐1} denote the L distinct intensity levels in a digital image of size M × N pixels, and let ni denote the number of pixels with intensity i. The total number, MN, of pixels in the image is MN = n0 + n1 + n2 + ,..., + nL‐1, where pi = ni/MN. For three classes consisting of three intensity intervals (which are separated by two thresholds) the between‐class variance (σB) is given by

σ2B ¼ P1 m1−mGð Þ2 þ P2 m2−mGð Þ2 þ P3 m3−mGð Þ2 (1) where

Table 1 Details of NAC Images Covering the CE‐4 Preselected Landing Area

NAC image ID Resolution

(meters per pixel) Incidence angle (°)

Solar azimuth angle (°)

M1220160190L 0.578 65.75 150.73 M143453659L 0.629 53.36 225.41 M143453659R 0.628 53.43 224.01 M161149639L 1.155 71.27 201.91 M161149639R 1.153 71.35 200.83 M161142858L 1.155 71.08 201.89 M161142858R 1.154 71.17 200.82 M134022629L 1.269 77.55 167.75 M134022629R 1.268 77.64 167.94 M180000082L 1.265 83.55 173.82 M180000082R 1.263 83.65 173.8 M115143943L 1.267 76.24 194.77 M115143943R 1.265 76.33 193.9 M128121241R 0.564 58.91 219.08 M1242491605L 0.82 55.89 229.45 M1242491605R 0.819 55.98 227.9 M180007222R 1.251 83.62 173.67 M178833263R 1.398 86.79 201.82 M1095330314L 1.319 84.73 173.98 M1095330314R 1.317 84.83 173.96 M189435642L 0.622 54.31 232.19 M1128338348L 0.658 67.75 155.39 M1095344559R 1.356 84.51 174.1 M180007222L 1.252 83.52 173.68 M171761396R 0.648 43.19 266.16 M1110639845R 1.234 86.39 176.84 M1145986900R 0.617 53.56 128.73

Note. NAC = narrow‐angle camera; CE‐4 = Chang'e‐4.

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P1 ¼ ∑ k1

i¼0 pi; P2 ¼ ∑

k2

i¼k1þ1 pi; P3 ¼ ∑

L−1

i¼k2þ1 pi (2)

and

m1 ¼ 1 P1

∑ k1

i¼0 ipi; m2 ¼

1 P2

∑ k2

i¼k1þ1 ipi; m3 ¼

1 P3

∑ L−1

i¼k2þ1 ipi (3)

The two optimum threshold values, k1 * and k2

*, are the values that maximize σB 2 = (k1, k2). In other words,

we find the two optimum thresholds by finding:

σ2B k * 1; k

* 2

� � ¼ max

0<k1<k2<L−1 σ2B k1; k2ð Þ (4)

Figure 2. (a) Lunar Reconnaissance Orbiter narrow‐angle camera mosaic of CE‐4 preselected landing area marked with a white box in Figure 1. The Lambert Conformal Conic Projection was used and some small gaps (white areas pointed out by yellow arrows) remained. (b) The image segmentation results of CE‐4 preselected landing area through a double‐ threshold Otsu method. CE‐4 = Chang'e‐4.

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The thresholded image is then given by g(x, y) = a, if f(x, y) < = k1 *; g(x, y) = b, if k2

* < f(x, y) < = k2 *;

g(x, y) = c, if f(x, y) > k2 *, where a, b, and c are the values standing for the dark area, flat area, and bright

area separately.

2.3. Image Segmentation Results

In order to ensure the consistency of illumination conditions in the segmentation region, the mosaic NAC image was divided into regular grids (or subimages) whose sizes were 500 pixels × 500 pixels. The gray values of each grid were transformed to [0–255] by the linear stretching method. The double‐threshold Otsu method mentioned previously was used to every grid to calculate the two optimum thresholds, k1

* and k2

*, and the original value (v) in each grid can be divided into the dark part (v < k1 *), the bright part

(k1 * < v < k2

*) and the flat part (v > k2 *). The image segmentation results of CE‐4 preselected landing area

were shown in Figure 2b. The black and white colors represented the dark and bright areas, which were uneven areas, while the light green color stood for the flat areas. There were several observations:

(1) PNTs identification. In Figures 3a and 3b, all the impact craters can be identified as dark and bright areas, and rocks (bigger than ~3.0 m, yellow arrows in Figure 3a and red arrows in Figure 3b) around impact craters can also be distinguished. In Figures 3c and 3d, there are many small ridges and troughs (yellow arrows in Figure 3c), which can be seen as risks of landing and patrolling for CE‐4 mission. Fortunately, these tiny undulating objects can be identified as dark and bright areas (red arrows in Figure 3d) using our method. Therefore, we can see that there are good classification results for CE‐4 preselected landing area by a double‐threshold Otsu method. The PNTs can be identified accurately and completely, and the left parts are the flat regions.

(2) Error analysis. In our paper, the double‐threshold Otsu method was used in each grid of CE‐4 prese- lected landing area, and there were two optimum thresholds (k1

* and k2 *) in each grid. The k1

* and k2

* of the adjacent grids may be inconsistent; thus, the segmentation results may be of discontinuity in the same object, which is located in several grids. In Figure 3f, the discontinuity (the horizontal yellow dotted line on the left) appears, on the edge between parts A and B coming from the same NAC image, due to the different segmentation thresholds of the two parts. In addition, parts A, B, and part C come from two different NAC images. Because of the different illumination conditions and segmentation thresholds, discontinuities (the yellow vertical dotted line on the right) also occur in their adjacent boundaries. Moreover, in the study area, there are several dark and bright areas due to compositional inhomogeneity, which can cause the flat areas to be mistakenly classified into undu- lating areas. As shown in Figures 3g and 3h, there is only the dark area (the yellow dotted polygon) with- out a corresponding bright area, indicating that the dark area maybe result from the compositional heterogeneity on lunar surface. Luckily, this type of brightness changes caused by compositional hetero- geneity is very rare in the study area and can be ignored.

(3) Result verification. In order to verify the accuracy of the image segmentation results, we evaluated the consistency between the traverse route of Yutu rover and the flat areas identified by our method at CE‐3 landing site. In Figures 3i–3k, we can see that the route (blue line) of Yutu rover fall into the flat area extracted by our method and is kept away from the dark and bright areas, which are inferred as PNTs. This comparison result shows a good consistency between a real route and our experimental segmentation results. Therefore, the double‐threshold Otsu method can be used to identify obstacles on lunar surface and ensure the safety of CE‐4 landing and patrolling tasks.

3. Safety Assessment for CE‐4 Preselected Landing Area 3.1. Calculating the Faps of Square Grids

In order to assess the safety of different locations, we divided the CE‐4 preselected landing area into regular square grids. Both the lander and the rover of CE‐4 were designed as a backup for the CE‐3 mission (Ye et al., 2017), and the flight process and working modes of CE‐4 were fully inherited from those of CE‐3 probe (Jia et al., 2018). Therefore, according to the CE‐3 landing process, the divided square grid size in the CE‐4 pre- selected landing area can be determined. The powered descent process of the CE‐3 mission includes stages of major deceleration, rapid adjustment, approach, hovering, obstacle avoidance, and low‐speed descent (Liu et al., 2014). The whole process lasted about 720 s. When CE‐3 probe descended to a height of about 100 m, the probe entered the hovering stage. Because the time taken by this stage was just 25 s, the

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Figure 3. (a and b) The NAC image and the segmentation results of a crater and several surrounding rocks (the yellow arrows). (c and d) The NAC image and the segmentation results of the small ridges and troughs (yellow and red arrows). (e and f) The discontinuities (the two yellow dotted lines) due to the different illumination conditions and seg- mentation thresholds in the same NAC image and two adjacent NAC images. (g and h) The brightness changes (the yellow dotted polygon) because of the compositional heterogeneity on lunar surface. (i–k) The CE‐3 landing site in the NAC image M181302794LC with a resolution of ~1.57 m, the route of Yutu rover, and the image segmentation results of the CE‐3 landing site. The boundaries of (a), (c), (e), and (g) are marked in the yellow boxes in Figure 2. NAC = narrow‐angle camera; CE‐3 = Chang'e‐3.

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motion of CE‐3 probe is small (~0.001° in longitude, from −19.5134° to −19.5125°). While in the whole descent process, the entire motion of CE‐3 probe is ~0.1097° in longitude, from −19.4027° to −19.5124°. According to the above analysis, the size of divided square grids used to evaluate safety was set to 0.01°. Based on the segmentation results described on Section 2, the Fap of each divided square grid with a size of 0.01° was calculated and was shown in Figure 4.

3.2. Determining the Fap Threshold for Lunar Safe Landing

After both flat areas and uneven areas were identified in a grid, the Fap of this grid can be calculated. The Fap is a factor that can be used to measure the safety for landing and traveling in the grid. In order to obtain the Fap threshold for the safe landing and traveling for CE‐4, here we calculated the Faps at the landing sites

of past successful lunar missions, including CE‐3, Apollo, Surveyor, and Luna series. Using the double‐threshold Otsu method, the Faps of the square grids, with sizes of 50, 100, and 200 m around the landing sites, were computed. The details of past successful landing sites and square grids are listed in Table S1 in the supporting information, and the image segmentation results in these square grids are shown in Figures S1–S13. The Faps in past successful lunar landing sites are shown in Table 2.

We can see that for the past successful landing sites, the Faps in square grids with a size of 200 m are all bigger than ~53.6%, except for CE‐3 land- ing site with a Fap of only ~35%. The CE‐3 probe landed on the rim of Zi Wei crater (~27–80 Myr old; Xiao et al., 2015). The diameter of this crater is ~450 m, which would have excavated ~40–50 m beneath the surface. The entire CE‐3 landing site was blocky and covered by the ejecta and big boulders of Zi Wei crater (Ling et al., 2015). Although CE‐3 landing area has the smallest Fap, the uneven areas in it do not occur randomly but tend to be clustered together. In Figure 3j, almost all the uneven areas were gathered near the left of CE‐3 landing site, and CE‐3 probe landed in the flat area on the right of the Zi Wei crater. Therefore, the distribution pattern of the uneven features in the landing area is also an important fac- tor for landing safety assessment. In this work, we only considered the Fap factor but ignored the distribution pattern of the uneven features in the landing area. According to Table 2, the average Fap of all successful land- ing sites was 58.7%. If CE‐3 landing site was excluded, the average Fap

Figure 4. The Fap of each divided square grid with a size of 0.01° in Chang'e‐4 preselected landing area, superposing on the narrow‐angle camera mosaic image. The five potential landing areas (yellow polygons) are marked with numbers 1–5, while the three least safe landing areas (red polygons) are marked with A–C.

Table 2 The Faps of Square Grids Around the Past Successful Lunar Landing Sites

Landing site Square size (m)

Fap (%)

Landing site

Square size (m)

Fap (%)

Luna 17 50 53.6 Apollo11 50 49.2 100 57.3 100 47.4 200 55.1 200 53.6

Luna 21 50 56.5 Apollo12 50 57.4 100 62.3 100 47.0 200 64.0 200 56.0

CE‐3 50 37.8 Apollo14 50 61.2 100 39.4 100 62.3 200 35.0 200 69.0

Surveyor1 50 65.3 Apollo15 50 44.4 100 74.3 100 63.2 200 71.2 200 62.8

Surveyor5 50 51.4 Apollo16 50 65.0 100 48.2 100 70.8 200 58.3 200 68.7

Surveyor6 50 59.7 Apollo17 50 70.3 100 54.2 100 66.9 200 52.8 200 71.7

Surveyor7 50 70.1 100 73.5 200 68.6

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increased to 60.6%. Therefore, we thought it was safe for CE‐4 landing in a grid if its Fap was bigger than 0.6.

3.3. Safety Assessment for CE‐4 Preselected Landing Area

According to the Fap of CE‐4 preselected landing area, the divided square grids can be classified into safe grid (Fap > 0.6) and unsafe grid (Fap ≤ 0.6). In Figure 4, the grids with blue and light blue colors were safe for CE‐4 landing, while the grids with red and light red colors were unsafe for CE‐4 landing. And the adjacent safe grids were merged, so that the range of CE‐4 preselected landing area can be greatly reduced. As shown in Figure 4, five PLAs (yellow polygons marked with numbers 1–5) were labeled. PLAs 1–3 were located on the right side of the preselected landing area, while PLAs 4 and 5 were located on the left of the preselected land- ing area. The details of the five PLAs were shown in Table 3. The average Faps of the five PLAs were all larger than 0.7 except for PLA 2. PLA 1 and PLA 5 were the best choices for CE‐4 landing because of their bigger areas and higher average Faps. In addition, three least safe landing areas (LLAs, red polygons marked with letters A–C) were labeled in Figure 4. These three LLAs with dense PNTs are not suitable for CE‐4 lander to land because of the lowest average Fap values. The details of the three LLAs were shown in Table 4.

4. Route Planning for CE‐4 Rover Moving From Current Grid to Target Grid

The CE‐4 Lunar Probe is comprised of a lander, a rover, and a relay satellite. After CE‐4 lands on the floor of Von Kármán crater, a rover will be released to travel around. The payload elements of CE‐4 rover contain a visible/near‐infrared imaging spectrometer, a ground penetrating radar and a panorama camera, etc. The rover should be able to carry out imaging, spectral and radar measurements. However, due to the limited field of view of the panorama camera, it is difficult for rover to select a long‐distance (several or tens of kilometers) and safe patrol route in real time. In this section, we proposed a route planning method, which took both the distance and security into account, for CE‐4 rover to dynamically generate a safe and short route from current grid A to target grid B. This method has two steps including route traversal and route planning.

4.1. Route Traversal

In this step, all the paths between grid A and grid B are traversed in a computer, and all passing grids in each path are saved in a file. First, a rectangle with a diagonal line AB is generated. The default is that grid A is in the upper left corner, otherwise the rectangle is turned over. We assume that the routes from grid A to grid B are in the rectangle AB and cannot be out of the range. And then taking grid A as the starting grid, a path set P containing all the paths is generated using a path traversal algorithm, which travels the whole rectangle AB in an order of the rightward, downward, and diagonal directions. The sketch map is shown in Figure 5 and pseudocode of path traversal algorithm is shown as below:

Pseudo code create a stack S create an array status[grid(m, n)]

dir[3][2] = {{0,1},{1,0},{1,1}}; //rightward, downward and diagonal direction //m and n are the row and column number of the grid, status[grid(m, n)] ==0 means this grid is //not be visited, while status[grid(m, n)]==1 indicates it has been traveled procedure PathTraverse(grid(i, j)):

if (i == m‐1 && j == n‐1) // a path has been found pop all grids from S and record this path; return;

if (i>= m ‖ j >= n) //out of range of the rectangle

▪ return;

Table 3 The Details of Five PLAs in CE‐4 Preselected Landing Areas

PLA Area (km 2 )

Number of divided square grid Average Fap

1 48 801 0.712 2 53 873 0.687 3 39.2 656 0.701 4 16.8 298 0.745 5 51.6 884 0.716

Note. PLA = potential landing area; CE‐4 = Chang'e‐4.

Table 4 The Details of Five LLAs in CE‐4 Preselected Landing Areas

LLA Area (km 2 )

Number of divided square grid Average Fap

A 78.1 1,317 0.558 B 61.9 1,036 0.543 C 125.6 2,110 0.522

Note. LLA = least safe landing area; CE‐4 = Chang'e‐4.

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for (int k=0; k < 3; k++) //travel in three directions

▪ ii = i + dir[k][0];

▪ ij = j + dir[k][1]; // the row and column number of the next travelled grid

▪ if (ii < m &&ij< n && status[grid(ii, ij)] ==0)

▪ status[grid(ii, ij)] =1; //this grid has been visited

▪ S.push(grid(ii, ij)); ▪//push this grid into the stack

▪ PathTraverse(grid(ii, ij)); // recursion

▪ status[grid(ii, ij)] = 0; // backtrack

▪ S.pop(); // three directions have been travelled and this grid pop from the stack end procedure

4.2. Route Planning

In this step, we selected the safer and shorter route from the path set P. (1) Removing the inappropriate paths. The paths including the grid with smaller Fap should be removed from the path set P. (2) Calculating the average Fap (AFap) of each path. The Faps of all grids on a path are summed up and then divided into the number of the passing grids in the path to obtain the average Fap. (3) Computing the normalized distance (ND) of each path. If traveling in the rightward and downward directions, the distance between current grid and next grid is the length of the grid. While if traveling in the diagonal direction, the

distance between the two grids is ffiffiffi 2

p times of the square grid's length. The distance of each path is normal-

ized to a range of 0–1.0 after divided into the longest distance from grid A to grid B, which is rowN + colN‐2 (the rowN and the colN are the row number and column number of the rectangle AB). (4) Weighted path planning. We think that safety and distance of one path are equally important for CE‐4 rover's traveling. By giving the equal weight 0.5 to safety and distance respectively, the weighted result (WR) of each path can be calculated by: WR = 1 − 0.5 * AFap + 0.5 * ND. A path in set P with the smallest WR is selected as the safer and shorter route from current grid A to target grid B.

For example, we assume that the rover wants to move from grid A (i = 0, j = 0) in PLA 1 to grid B (i = 11, j = 16) in PLA 2. The paths derived from our weighted path planning method are shown in Figure 6. The rectangle AB (the red rectangle in Figure 6) is a 12 × 17 grid network. Among all paths between grid A and grid B, the shortest route with the smallest ND is marked out with the black arrows in Figure 6b, the safest route with the biggest AFap is marked out with the red arrows in Figure 6b, and the best weighted path with the smallest WR is shown with blue arrows in Figure 6b. In addition, if the rover wants to add an inter- mediate grid C (i = 3, j = 10, Figures 6a and 6b) in its route, that is to say, the rover travels from grid A to grid C and then moves to grid B. In such a situation, the all paths from grid A to grid B are found out through our route traversal method. The paths containing grid C are selected and their WRs are calculated. The path with the smallest WR is the best path from grid A to B going through grid C, which is shown with green circles in Figure 6b. The details of the four paths derived from our method are shown in Table 5.

Figure 5. The sketch map of our path traversal algorithm. Panels (a) and (b) show the results of traveling in a 4 × 4 net- work with no obstacle and four obstacles. The black, red, and blue arrows show the first, second, and last path from grid A to grid B using our algorithm.

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5. Summary and Future Work

China's CE‐4 probe will explore the South Pole‐Aitken basin at the end of 2018 to achieve the first on‐site exploration of the lunar farside. The south of the Von Kármán crater is chosen as its PLA. However, the successful experience of CE‐3 landing and patrolling in Mare Imbrium in 2013 could not be directly applied to the CE‐4 mission, because of the more rugged far side of Moon, which leads to the difficulties of safe

Table 5 The Details of Four Paths in Figure 6

Path ND (times of grid length) AFap(%) WR Description

1 13 þ 7 ffiffiffi 2

p 22:8995ð Þ 0.730 1.058 The shortest path from A to B

2 21 þ 3 ffiffiffi 2

p 25:8284ð Þ 0.757 1.082 The safest path from A to B

3 13 þ 7 ffiffiffi 2

p 22:8995ð Þ 0.734 1.043 The best path from A to B

4 15 þ 6 ffiffiffi 2

p 23:4853ð Þ 0.734 1.060 The best path from A to B through C

Note. ND = normalized distance; WR = weighted result.

Figure 6. (a) The Fap map of the study area, marked in the white rectangle in Figure 4, superposing on the narrow‐angle camera mosaic image. Grid A in PLA 1 and grid B in PLA 2 are current grid and target grid. Grid C is an intermediate grid. (b) Route planning results. The black arrows show the shortest path, while the red and blue arrows show the safest path and the best path from grid A to grid B. The green circles show the best path from grid A to grid B going through grid C. Number i and j are the row and column numbers of the grid in rectangle AB. PLA = potential landing area; ND = normalized distance.

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landing and traversing. Moreover, due to scale dependence and smoothing effects, smaller topographic features in the CE‐4 preselected landing zone could not be displayed through the topographical studies pre- viously derived from DEM data with low‐resolution (~59 m per pixel). In this paper, we proposed a method to identify PNTs and choose PLAs for CE‐4 probe using LRO NAC images with a decimeter resolution. This method can also be applied to select the safe landing areas for China's CE‐5 and Mars exploration missions in the future.

PNTs on the surface of a planet represent an obvious hazard to landing spacecraft and a potential impedi- ment to traveling. Identifying the PNTs at PLSs with remote sensing data is thus critical to the success of a task. On lunar surfaces, shadows and bright areas in remote sensing images or in situ photographs are caused by the presence of raised or depressed features, which are interpreted as PNTs, that is, uneven areas. In this paper, the double‐threshold Otsu method was used to calculate the two optimum thresholds, k1

* and k2

*, and the original values (v) in the NAC mosaic image can be divided into the dark parts (v < k1 *), the

bright parts (k1 * < v < k2

*), and the flat parts (v > k2 *). The image segmentation results of CE‐4 preselected

landing area were shown in Figure 2b. The black and white colors represented the dark and bright areas, which were uneven areas, while the light green color stood for the flat areas.

In order to obtain the Fap threshold for the safe landing and traveling, we calculated the Faps at the landing sites of past successful lunar missions, including CE‐3, Apollo, Surveyor, and Luna series. The average Fap of all successful landing sites was 58.7%. If CE‐3 landing site was excluded, the average Fap increased to 60.6%. Therefore, it is safe for CE‐4 landing in a grid if its Fap is bigger than 0.6. According to the Fap of CE‐4 preselected landing area, the divided square grids can be divided into safe grid (Fap > 0.6) and unsafe grid (Fap ≤ 0.6). The adjacent safe grids were merged, and the range of CE‐4 preselected landing area can be greatly reduced to five PLAs. The PLA 1 and PLA 5 are the best choices for CE‐4 landing because of their bigger areas and higher average Faps.

After CE‐4 lands on the floor of Von Kármán crater, a rover will be released to travel around. Due to the limited field of view of the panorama cameras, it is difficult for rover to select the long‐distance and safe route in real time. In this paper, we proposed a route planning method, which took both the distance and security into account, for CE‐4 rover to dynamically generate a safer and shorter route between current grid A and target grid B. First, all the paths between grid A and grid B are traversed in a computer, and all passing grids in each path are saved in a file. By giving the equal weight 0.5 to safety and distance respectively, the weighted result of each path can be calculated by WR = 1 − 0.5 * AFap + 0.5 * ND. A path with the smallest WR is selected as the safer and shorter route from current grid A and target grid B.

In the future, we plan to continue the following work: (1) In this paper, we only used the Fap factor to evaluate the grid safety without considering the concentration degree of the uneven areas. If the grid has a smaller Fap but clustered uneven objects, just like the CE‐3 landing site, this grid is still safe for lander landing and rover traveling. We will continue to improve the grid safety evaluation method by taking both the Fap and concentration degree into account. (2) Due to time and energy constraints, we performed the path traversal in only three directions; in fact, there are eight directions when the rover moves from one grid to another next grid. Moreover, because of the huge computation, the size of the divided square gird in CE‐4 preselected landing area was only 0.01°. In the future work, we will further divide the grid into 0.005° and 0.001° and obtain more accurate security evaluation results.

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