Selection of Lunar South Pole Landing Site Based on Constructing and Analyzing Fuzzy Cognitive Maps

Abstract

The Permanently Shadowed Regions (PSRs) of the lunar south pole have never been directly sampled. To explore and discover lunar resources, the Chinese lunar south pole exploration mission is scheduled to land in direct sunlight near the PSR, where sampling and analysis will be carried out. The selection of sites for lunar landing sampling sites is one of the key steps of the mission. The main factors affecting the site selection are the distribution of PSRs, lunar surface slopes, rock distribution, light intensity, and maximum temperature. In this paper, the main factors affecting site selection are analyzed based on lunar multi-source remote sensing data. Combined with previous engineering constraints, we then propose a comprehensive multi-factor fuzzy cognition and selection model for the lunar south site selection. An analytical model based on a fuzzy cognitive map algorithm is also established. Furthermore, to make a preliminary landing area selection, we determine the evaluation index for the candidate landing areas using fuzzy reasoning. Using the proposed model and combined scoring index, we also verify and analyze the prominent impact craters at the lunar south pole. The scores of de Gerlache (88.48°S 88.34°W), Shackleton (89.67°S 129.78°E), and Amundsen (84.5°S, 82.8°E) craters are determined using fuzzy interference as 0.816, 0.814, and 0.784, respectively. Moreover, using our proposed approach, we identify feasible landing sites around the de Gerlache crater close to the PSR to facilitate discovery of water ice exposures in future missions. The proposed method is capable of evaluating alternative landing zones subject to multiple engineering constraints on the Moon or Mars based on the existing data.

1. Introduction

As the closest celestial body to the planet Earth, the Moon is the first choice for space exploration [1]. To date, about 118 probe missions have been carried out and more than 20 probes have explored the surface of the Moon [2]. In recent years, the lunar polar region has become the focus of the international lunar exploration. In addition to its unique geographical location [3,4], scientific value, and research significance, the lunar polar region has rich mineral resources [5,6] and water ice [7,8,9].

The successful sampling of the lunar surface carried out by Chang’E-5 indicated that the Chinese lunar exploration program has entered the next phase [10]. In the Chang’E-7 mission [11], the lunar lander carrying a rover and a small landing module is planned to land in the sunlit area near the PSRs located at the lunar south pole so that the rover can obtain solar energy [12]. Shorter distances to the nearby PSR sampling points make sampling and analysis more feasible. Therefore, selecting landing sites at the south pole of the Moon and planning corresponding exploration routes are significant for this mission.

Several studies into landing sites on the Moon’s south pole have been carried out over the past few years. In such studies, the available remote sensing datasets were analyzed to suggest potential areas of interest for future lunar missions, and these areas include together with smaller regions located near Cabeus, Amundsen, Ibn Bajja, Wiechert J and Idel’son craters [13,14,15]. Qiao et al. [16] also studied the global albedo of the Moon at 1064 nm from the Lunar Orbiter Laser Altimeter (LOLA) at the inside and outside of the PSR for the flat polar region. By excluding the influence of illumination, temperature, composition, and other factors, they concluded that the abnormal albedo inside and outside the PSR is likely due to the existence of water ice and similar work has been conducted by Fisher et al. [17]. Therefore, the Amundsen crater at the lunar south pole was recommended as a suitable landing zone for future explorations.

Furthermore, using multi-parameter analysis, Lemelin et al. [18] identified the best possible landing sites for returning volatile-rich samples from the lunar poles. They pointed out two such sites in the lunar south region (Shoemaker and Faustini craters) and two in the lunar north region (Peary and an area between Hermite and Rozhdestvensky W craters). By relaxing the restrictions, they further identified five additional sites in the south polar region (Haworth, de Gerlache, and Cabeus craters, as well as an area between Shoemaker and Faustini and north of Amundsen crater), and three additional sites in the north polar region. Nevertheless, these sites are all within the PSR, thus extremely challenging to access using solar-powered spacecraft.

NASA also commissioned the Volatile Specific Action Team to identify landing sites for future missions. The Lunar Exploration Advisory Group (LEAG) proposed an Area of interest (ROI) near Cabeus and Shoemaker in the south polar region based on the study of Lemelin et al. [18], where they changed the threshold and adjusted the limits of the visibility of the sun and earth. In the analysis, they considered the following two criteria. The first criterion was that the H abundance estimated from the Lunar Prospector neutron spectrometer (LPNS) data is higher than 150 PPM. The second was that the annual surface temperature of the landing site is less than 110K, has a moderate slope (< 10), and is less than 1 km from the PSR.

The above studies rely on expert knowledge for landing site selection without a comprehensive and reliable algorithm. To address this issue, in this paper, we propose a comprehensive multi-factor fuzzy cognition and selection model for the south pole site to systematically identify future landing sites. In our method, we use lunar multi-source remote sensing data and focus on the requirements of the lunar south pole mission. The contributions of this work are as the follows:

• We investigate the main factors affecting site selection based on analyzing lunar multi-source remote sensing data, combined with previous actual engineering constraints, and preliminary screening of the conditions of future lunar south pole exploration areas.
• A comprehensive multi-factor fuzzy cognition and selection model is proposed to identify landing sites for future missions, combined with score rules, the algorithm quantitatively evaluates three regions (de Gerlache, Shackleton, and Amundsen) and eight sites for other missions subject to a range of engineering constraints and mission requirements.
• For the validation results of the model, we take the future CE-7 lunar south pole exploration mission as an example to conduct a route analysis of selected potential landing sites. We analyzed the indicators (slope, light, and temperature) to verify the model’s reliability further.

The rest of this article is organized as follows. Section 2 introduces the lunar south pole area datasets and analytical methods for calculating various factors. In Section 3, the results of the lunar shadow area and other engineering factors are analyzed and discussed with the aim of finding candidate landing sites and mission target points. Finally, in Section 4, conclusions are presented followed by suggestions for future work.

2. Materials and Methods

Vast amounts of remote sensing data have been collected during the last several decades, providing crucial information about the Moon’s south pole. In this paper, we used ESRI ArcGIS software to collect global data products and a Geographic Information System (GIS) and python for combined analysis.

2.1. Study Area

The lunar south pole at the edge of the Aitken Basin has rugged and complex terrain, including several impact craters [19,20]. This study covers the high latitude region of the Moon (above 80°S) with elevations ranging from −6325 m to +7010 m. The overall elevation difference is about 14 km with large fluctuations and an average elevation of about −1400 m at the south pole. Figure 1 shows the Shackleton, de Gerlache, Sverdrup, Slater, Faustini, Shoemaker, and Haworth craters around the south pole. The outer ring also includes the Nobile, Amundsen, Idel’son L, Wiechert E, Wiechert J, Cabeus, Mal, and several other craters. These craters have diameters ranging from 20 to 150 km. Most craters have flat inside surfaces, except for a few craters with central peaks, e.g., the Amundsen crater [14].

2.2. Data

The details of the data used in this study are presented in

Table 1. The data used in this paper.

Spacecraft	Payload	Data Type	Resolution	Range	Application Section	Projection Method
CE-2	CCD	DEM	20 m/pixel	80°S–90°S	2.3.2/3.2	Polar stereographic projection
		DOM	7 m/pixel	Local area	2.1/3.3
LRO	LROC	Images	1 m/pixel	Local area	2.3.3/3.4
	LOLA	DEM	5 m/pixel	Local area	3.4
			240 m/pixel	75°S–90°S	2.3.1/3.2
	Diviner	Thermal infrared	200 m/pixel	80°S–90°S	3.2

. We used a multi-source data analysis method to model and analyze the data collected by CE-2 and the Lunar Reconnaissance Orbiter (LRO). The polar stereographic projection is employed as the projection method.

The CE-2 20-m resolution digital elevation model, and 7-m resolution digital orthographic images were produced based on the stereo images obtained by the CE-2 stereo camera CCD at an orbital altitude of 100 km. The LROC data was also included in our analysis, especially the wide-angle camera (WAC) global mosaic at 100 m/pixel, and the narrow-angle camera (NAC) polar mosaics at ~1 m/pixel [21]. We also estimated the slope steepness in the target areas using the digital elevation model (DEM) produced from LRO/LOLA data [22]. The Diviner lunar radiometer, which is one of seven instruments on board the LRO, includes measurements of lunar surface thermal radiation and solar reflectivity with resolutions of 60 m/pixel [23].

2.3. Methods

Compared with the middle and low latitude regions, the south pole of the Moon has significantly different characteristics related to terrain, temperature, illumination [24]. These characteristics significantly affect the landing missions. The objective of lunar south pole missions is to land at a site near the PSRs and conduct sampling and analysis in the PSRs. Hence, it is essential to study the characteristics such as slope, illumination, the distribution of rocks, and maximum temperature data of the landing and exploration area for this mission. Here, we construct fuzzy cognitive maps to analyze the data and identify the potential landing site. A flowchart of the proposed method is presented in Figure 2.

2.3.1. South Pole Illumination Model

The study of the illumination conditions in the lunar polar region is of great significance, especially for landing on the Moon. It also provides basic information for the sensor design of probes, site selection for lunar surface bases, and further study of the existence of water ice.

The surface of the Moon is a complex terrain with distinct highlands that significantly affect the illumination in different regions. In previous works, the maximum angle of elevation database was constructed under a specific angular resolution [25,26]. This method reduces the calculation time. However, due to the influence of angular resolution, it is unable to accurately determine the maximum terrain height angle in a specific incidence direction. In this paper, the maximum topographic height angle method is used to check whether a specific location on the Moon is illuminated. The core of this method is to compare the solar height angle of the following month point with the maximum topographic height angle at a particular time. The flowchart of this method is presented in Figure 3.

The angle of the sun or (the elevation of the sun) refers to the angle of the sun relative to the ground plane. For a certain point on the Moon, the sun refers to the incident direction of the sun. The sun’s height is the angle between the direction of sunlight incidence and the ground plane. The height of the sun changes with time.

As shown in Figure 4, φ is the solar altitude angle from point M. Its calculation process is as follows:

$$\alpha =\arcsin \left[\frac{R\sin \beta }{{\left(R_{\mathrm{s}-\mathrm{m}}^2+R^2-2R_{\mathrm{s}-\mathrm{m}}R\cos \beta \right)}^{1/2}}\right]$$

(1)

$$\beta =\arccos \left[\sin {\phi }_M\sin {\phi }_{S^{\prime }}+\cos {\phi }_M\cos {\phi }_{S^{\prime }}\left.\times \cos \left({\lambda }_M-{\lambda }_{S^{\prime }}\right)\right]\right.$$

(2)

where (φ_M,λ_M) and (φ_S′,λ_S′) are the position coordinates of the calculated points M and S’ under the sun, respectively. Furthermore, R is the Moon’s mean radius, and Rs-m denotes the distance between the sun and the Moon. The solar altitude angle of point M is obtained using (1) and (2), hence:

$$\phi =\frac{\pi }{2}-\left(\alpha +\beta \right)$$

(3)

Considering the apparent radius of the sun, the height angle is:

$$\phi \prime =\phi +0.27$$

(4)

A positive solar altitude angle indicates that the corresponding area is within the range of solar irradiation. Similarly, a negative solar altitude angle implies that the area deviates from solar irradiation. In other words, the area is a permanently shadowed region and thus solar illumination is inaccessible.

2.3.2. Lunar Surface Slope

The slope affects the soft landing and patrol direction of the probe. The slope mainly affects the probe’s descent process, fuel loss, and stability upon touching the lunar surface. During the patrol, the slope also affects the safety of the patrol route. Therefore, considering the safety of landing and patrol movement, the landing surface needs to be either flat or with a minimal slope. In selecting landing sites for Chinese lunar missions, the average terrain gradient of landing zones should not exceed 8° [2,10].

The existing lunar DEM indicates craters of different sizes on the surface of the Moon. The lunar landing site and exploration zone need to have a relatively gentle slope to enable exploration of the PSRs. The terrain gradient can be calculated from the slope of each cell of the lunar DEM grid as the follows:

$${\theta }_{w-e}=\frac{\left({\theta }_{m+1,n-1}+2{\theta }_{m,n-1}+{\theta }_{m-1,n-1}\right)-\left({\theta }_{m+1,n+1}+2{\theta }_{m,n+1}+{\theta }_{m-1,n+1}\right)}{8\times Cellsize}$$

(5)

$${\theta }_{s-n}=\frac{\left({\theta }_{m+1,n+1}+2{\theta }_{m+1,n}+{\theta }_{m+1,n-1}\right)-\left({\theta }_{m-1,n+1}+2{\theta }_{m-1,n}+{\theta }_{m-1,n-1}\right)}{8\times Cellsize}$$

(6)

$$\theta =\arctan \sqrt{{\theta }_{{}_{s-n}}^2+{\theta }_{{}_{w-e}}^2}$$

(7)

where Cellsize is the resolution of each grid point and m and n denote the cells’ row and column numbers, respectively. For a suitable lunar landing site, the slope should be subject to the following constraints:

$$\theta <{\theta }_{\max }$$

(8)

where θ_max is the maximum slope, which is set to 8° for the CE mission [11]. The schematic diagram of the above calculations is shown in Figure 5.

2.3.3. Rock Abundance

Rocks should be avoided at the landing area as they might damage the landing buffer mechanism of the platform. Rocks should also be avoided between the engine nozzle of the landing platform and the ground after the landing. They can also damage the rover’s chassis structure and affect its mobility.

Depending on the image resolution, the smallest boulders that can be recognized with confidence in the NAC images are in the order of ~1–2 m. We located and counted the boulders on NAC images using CraterTools [27] and Crater Helper Tools developed for ArcGIS. These software packages have been shown to be most effective for counting and recording boulders on the LROC NAC images [28].

We used LRO NAC images to characterize boulder populations around six small (<1 km) young (<200 Ma) impact craters near the CE-7 landing site. The rock abundance model follows the following format [29]:

$$R_m\left(d\right)=m{e}^{-\left(0.5648+0.01285/m\right)/d}$$

(9)

where m denotes the rock abundance, and R_m(d) refers to the areal fraction of rocks with a diameter larger than d, d = 3 m. The model in (9) describes the overall cumulative fractional area (CFA) of rocks versus their diameters.

2.3.4. Constructing and Analyzing Fuzzy Cognitive Maps

A cognitive graph is a graph model expressing the causal relationship between system concepts. Kosko [30] introduced the concept of a fuzzy measure and based on that proposed a fuzzy cognitive graph model. Since the fuzzy measure integrates the characteristics of fuzzy logic theory and neural networks, it enables causal relationship expression and reasoning [31,32,33].

To identify the location of the landing site at the south pole of the Moon, we propose a comprehensive multi-factor fuzzy cognition and selection model. This model combines PSR distribution (C1), lunar surface slope (C2), rocks distribution (C3), illumination intensity (C4), and maximum temperature (C5), as the conceptual node geometry E=={C1, C2, C3, C4, C5}. The relational weight matrix W=[Wij]_5×5 is also established, where the relational weight matrix forms the directed connection. The constructed fuzzy cognitive map is shown in Figure 6.

Based on previous analyses of constraints, combined with planetary science expertise, the importance ranking is based on the considerations presented in

Table 2. The order of significance of the engineering constraints.

Restrictive Factors			Significance Ordering
Scientific Targets	PSR	Square measure	1
Environmental conditions	Slope	2–10 m baseline	2
	Rock distribution	Rock abundance	3
	Illumination condition	Illumination intensity	4
	Surface thermal environment	Temperature	5

.

For the lunar south exploration mission, due to terrain limitations, the closer the distance to the permanently shaded area, the better. The fuzzy membership function of C₁ can be expressed as:

$$C_{1i}=\left\{\begin{array}{c}\frac{S_{\max }-S_i}{S_{\max }},0\le S_i<S_{\max }\\ 0,S_i\ge S_{\max }\end{array}\right.$$

(10)

S represents the distance between the site selection point and the permanent shadow area, combined with the engineering requirements of the lunar south pole exploration mission [11], and S_max is the maximum distance, set to 8 km.

For the lunar surface, the flatter the terrain, the more suitable the landing site. A site with a slope exceeding the threshold, θ_max, is not a suitable landing site. Therefore, the fuzzy membership function of C₂ is expressed as:

$$C_{2i}=\left\{\begin{array}{c}\frac{{\theta }_{\max }-\left|{\theta }_i\right|}{{\theta }_{\max }},0\le \left|{\theta }_i\right|<{\theta }_{\max }\\ 0,\left|{\theta }_i\right|\ge {\theta }_{\max }\end{array}\right.$$

(11)

When selecting landing sites for Chinese lunar missions [2,10], the slope should not exceed 8°, hence θ_max = 8°. The fuzzy membership function of C₃ is expressed as:

$$C_{3i}=\left\{\begin{array}{c}\frac{D_{\max }-D_i}{D_{\max }},0\le D_i<D_{\max }\\ 0,D_i\ge D_{\max }\end{array}\right.$$

(12)

D represents the rock abundance of the site selection point with altered topography. D_max is the maximum rock abundance, which is set to 20% [29]. The fuzzy membership function of C₄ can be also expressed as [34]:

$$C_{4i}=\left\{\begin{array}{l}\frac{1}{(b-a)\times T}\times \left(t_s-a\times T\right),b\times T<t_s\le a\times T\\ \frac{1}{b\times T}\times t_s,0<t_s\le b\times T\\ 0,t_s=0or{t}_s>a\times T\end{array}\right.$$

(13)

where T is the total time window, t_s is the illumination coverage time, a(0 ≤ a ≤ 1) is a scaling coefficient corresponding to T, and b(0 ≤ b ≤ a) is a scaling coefficient indicating the most suitable landing time, a is set to 0.3 and b is set to 0.15 according the time coverage of sunlight in craters [35]. The fuzzy membership function of C₅ is expressed as:

$$C_{5i}=\left\{\begin{array}{c}\frac{K_{\max }-K_i}{K_{\max }},0\le K_i<K_{\max }\\ 0,K_i\ge K_{\max }\end{array}\right.$$

(14)

where K is the temperature and K_max is the annual maximum temperature, set to 110 K [17].

Each variable includes four triangle membership functions, where the transition between functions is smoother and more stable. Feasible landing sites are classified as Highly feasible (HF), Intermediate feasible (IF), Low feasible (LF), and Infeasible (IN). The membership functions are shown in Figure 7. Considering, for example, the illumination intensity factor:

We establish the fuzzy allocation matrix (FAM), also referred to as the rule database. The specific values of the above constraints are obtained by analyzing the terrain images of different alternative landing sites. In the analysis, the central latitude of the landing zone, the coverage ratio of the baseline slope, the area of permanent shadow area, and the proportion of rock abundance are considered as the input parameters to evaluate the impact of the slope (S), maximum temperature (T), light intensity (I), and rock distribution (R). The order of engineering constraints introduced above and the combination of different constraints directly affect the establishment of fuzzy rules. The Mamdani minimum fuzzy implication rule [36,37] is shown in Figure 8 and is expressed as:

$${\mu }_R(x,y)=\min {\mu }_A(x),{\mu }_B(y)$$

(15)

where µ_A(x) and µ_B(y) denote the membership value x to the linguistic term A and the membership value y to the linguistic term B, respectively. For example, C₁ and C₂, C₁ and C₃, and so on.

We then aggregate the activated membership functions by applying the family Einstein Sum [38] operation, as shown in Figure 9 and expressed as:

$$f(x,y)=\frac{(x+y)}{\left(1+x\times y\right)}$$

(16)

Aggregation of the membership function and calculating the numerical weight of all concept pairs in the data returns a pandas data frame with the calculated weight. The defuzzification of the aggregated membership functions are shown in Figure 10.

FCM is an inference network that represents knowledge and reasoning using cyclic digraphs, and it can implement tasks such as modeling, analysis, decision making, and forecast by combining fuzzy logic with networks. The dynamics of the specified FCM are examined by simulating its behavior through discrete simulation steps. In each simulation step, the concept values are updated according to the Kosko method [30]:

$$A_i^{t+1}=f\left({\displaystyle \sum _{j=1}^n{A}_j^t\times W_{ji}}\right)$$

(17)

where A_j^t is the value of concept j at the simulation step t, W_ji is the causal impact of concept j on concept i, and W is the weight matrix.

Using the dynamics, a FCM diagram was constructed, as displayed in Figure 11. Factor inputs can be converted to a single output through the controller.

For a lunar south site, if C_1i = 0, C_2i = 0, C_3i = 0, C_4i = 0 or C_5i = 0, the comprehensive evaluation index Score is 0. For other sites, the comprehensive evaluation index Score is calculated from the fuzzy rule:

$$Score={\displaystyle \sum _{j=1}^5{\omega }_j{y}_{ij}}$$

(18)

$${\displaystyle \sum _{j=1}^5{\omega }_j=1,y_{ij}\in \left[0,1\right]}$$

(19)

where y_ij is the normalized value of the j evaluation index of the i pixel; and ω_j is the weight of the j evaluation index. The comprehensive evaluation index is distributed in the interval [0, 1], and the larger the value, the higher the reliability of site selection.

3. Results and Discussion

3.1. Effects of Permanently Shadowed Regions on Lunar South Pole Siting

In this paper, we use LOLA DEM data [25] for modeling the lighting and calculating the distribution range of the permanent shadow area in the lunar surface polar region. The results are illustrated in Figure 12.

Given the principle of PSR formation, they are generally distributed inside impact craters. Figure 12 shows that the PSRs in the south polar region are widely distributed in the central areas including the Shackleton, Faustini, Haworth, Shoemaker, de Gerlache, and Sverdrup craters. The area of these PSRs is large and some cover the craters almost completely.

3.2. Influence of Environmental Conditions on the Lunar South Pole Location

For the Chinese lunar landing missions, the average terrain slope of landing zones should not exceed 8°. The data adopted in this section are the local data of Chang ‘E-2 DEM 20 m/pixel and LRO LOLA DEM 5 m/pixel. Therefore, in Figure 13, the areas with a slope lower than 8° are shown in green, 8–15° in cyan, 15–25° in light yellow, 15–25° in orange, and above 35° in red. Above 80°S of the south pole, the average, maximum and minimum slopes are 9.5°, 80°, and 0°, respectively. Figure 13 indicates that the slope in the majority of areas is, in fact, less than 8°. The walls and edges of the craters have much higher slopes and the slopes are lower in crater bottoms and other areas.

For instance, the Shackleton impact crater (Figure 13f) has a 7 km wall with a central peak inside the crater with a significant slope. Its maximum, minimum, and average slopes are 62.5°, 0°, and 23°, respectively. The slope is mainly between 15° and 35° where the pit wall has the highest slope and accounts for a significant proportion of the whole area. The central peak of the pit bottom has a high slope. The rest is relatively flat, with a slope below 8° accounting for about 12% of the area. The rest of the analysis is shown in

Table 3. Slope analysis results of impact craters in the lunar south pole areas.

Name	Pit Area	Maximum Slope	Minimum Slope	Average Slope	Ratio Less Than 8°
Amundsen	2500 km2	77°	0.4°	10°	48%
de Gerlache	49 km2	61.5°	0.9°	15.4°	27%
Malapert	490 km2	63°	1.3°	8.7°	57%
Nobile	260 km2	64°	1.2°	14°	27%
Shackleton	37 km2	62.5°	0°	23°	12%
Shoemaker	603 km2	65.3°	0°	11.6°	35%

.

The illumination data used in this paper is the average illumination map obtained from [25]. The data in [22] used the high-resolution laser altimeter data of the LRO to simulate the illumination conditions in the lunar polar region (Figure 14). The pixel values in Figure 14 represent the proportion of time that the sun is visible from a given position.

Figure 14 shows that the average illumination intensity at the bottom of Amundsen, Malapert, and Nobile impact craters is continuously low. The Shoemaker, Shackleton, and de Gerlache impact craters have zero illumination inside and a good level of illumination outside the craters. The high illumination zone is mainly distributed near the northwestern edge of the de Gerlache impact crater (87.1°W, 88.5°S) and the Shackleton impact crater (0°E, 89.9°S) edge and the ridge, where it connects to the Sverdrup crater (152°W, 88.5°S). These are consistent with previous studies in [25,39,40]. The area with greater than 80% light intensity at the lunar south pole covers an area of about 3.99 km² with a maximum light intensity of 90.52% at the Shackleton edge (−137.1875°E, 89.453125°S) within 18.6 years. Another similar area exists near the Shackleton impact crater edge (54.9375°E, 89.796875°S), with a relatively small area (about 0.48 km²) and an average illumination of 80.75%.

The Diviner lunar radiometer aboard the LRO has been mapping the Moon’s infrared radiation since July 2009 using seven spectral channels ranging from 7.55 to 400 μm with a spatial resolution of 200 m. Using the radiometer’s data, the polar stereoscopic projection map of the maximum temperature distribution of the lunar south pole region has been generated based on the accumulated data from the last ten years [41]. This area is of an essential reference value for lunar south pole missions.

Figure 15B,C show annual maximum temperature data for 90°W–90°E and 0°W–180°W, respectively. The cool zones are 50 km from the de Gerlache crater, 31 km from the Shackleton crater, 40 km from the Faustini crater, and 50 km from the Amundsen crater. Figure 15 also shows a warmer zone at points 22 km, 35 km, and 45 km from the Haworth crater. The profile in Figure 15 shows that the temperature of the south pole changes dramatically with temperature differences reaching 200 K in some areas. This is mainly attributed to the impact of topography and landform. On the higher grounds, the area outside the impact crater can receive sunlight, resulting in the temperature reaching 300 K. In contrast, the areas inside the impact crater receive less sunlight, resulting in the temperature falling below 100 K. The temperature of the Shoemaker, Faustini, and Shackleton craters are in the ranges of 70–109 K, 70–95K, and 89–106 K, respectively. These results show that the areas with a temperature below 110 K at the Moon’s south pole are mainly located in the impact craters and roughly correspond to the areas with permanent shadow.

3.3. Application of the Proposed Evaluation Model

The initial values of the concept nodes are fed to the FCM model of the lunar south pole landing zone. We set the number of reasoning iterations to eight. After eight iterations of reasoning, the model system reached equilibrium with each conceptual node displaying stable values. The data value of the model iteration is then derived to obtain the stable value at the equilibrium state, as shown in

Table 4. Initial and stable values. The initial value is obtained by calculating the initial weight of each factor in Section 2.3.4. The stable value represents the optimal value of the system.

Node	C1	C2	C3	C4	C5
Initial value	0.412	0.707	0.607	0.783	0.314
Stable value	0.624	0.698	0.581	0.714	0.701
Difference value	0.212	0.009	0.026	0.069	0.387

. The initial and stable values are also shown in Figure 16.

Figure 16 shows that the optimal location of the lunar base is closely related to five factors. It can be seen from Figure 16 that the fuzzy cognitive map converges to a stable region after five iterations of the algorithm. It is also can be seen that C1 and C5 are improved, whereas C2, C3, and C4 are decreased and then became stable. Based on the convergence curve, the weight convergence values of illumination intensity (C4), maximum temperature (C5), and lunar surface slope (C2) were 0.714, 0.701 and 0.698, respectively.

In contrast to previous lunar exploration and landing zones, at the south pole of the Moon, the sunlight is almost parallel to the lunar surface, forming unique lighting conditions with both permanent shadow areas and long-term continuous light areas. The light is easily blocked by the terrain, which increases the difficulty of selecting the landing zone. Due to these conditions, landing zones should be selected at high altitudes with continuous light, areas which are often found on the edge of impact craters or the top of mountains. The rugged terrain also poses challenges for a subsequent soft landing and patrol detection. The biggest highlight of the lunar south pole emplacement exploration is the identification of water ice emplacement in the permanently shadowed area. Considering this scientific objective, the landing area should not be too far away from the permanently shadowed area of the target. On this basis, a local area with relatively flat terrain should be selected to ensure landing safety as much as possible.

Based on the above analysis, three areas and eight landing sites are initially selected as alternative areas. These areas are highlighted using red boxes in Figure 17. The evaluation index score adopts values in [0, 1] (Section 2.3.4. membership functions and Section 3.3 weights), and the higher the index, the more suitable the site. The evaluation results are presented in

Table 5. The evaluation index parameters for the red box areas in Figure 17.

	Shackleton			Amundsen			de Gerlache
ROI	a1	a2	a3	b1	b2	b3	c1	c2
Latitude	89.793°S	89.782°S	89.961°S	84.735°S	85.129°S	84.253°S	87.984°S	88.035°S
Longitude	26.73°E	156.36°W	145.25°W	90.82°E	85.61°E	95.78°E	86.01°W	77.25°W
Slope	7.9°	7.3°	2.2°	0.6°	1.3°	3.1°	5.3°	4.1°
Rocks distribution	11.7%	7.8%	8.3%	7.2%	9.2%	8.5%	6.8%	2.6%
Average illumination intensity	41.53%	51.91%	52.73%	30.51%	27.41%	25.27%	42.12%	50.14%
Average maximum temperature	147 K	131K	151 K	85K	104K	96K	113K	146k
Score	0.736	0.745	0.814	0.784	0.701	0.651	0.758	0.816

.

Table 5 shows that the de Gerlache, Shackleton and Amundsen craters have a maximum score of 0.816, 0.814 and 0.784, respectively; thus, the first two craters are preferred. This, however, does not necessarily mean the Amundsen crater is unfavorable. Note that the time coverage of the earth disk observations at the right site can be affected by the topography, as shown in Figure 17. For different launch times for different tasks, local illumination would vary, which also affects the selection based on illumination. For the Shackleton crater at 89.782°S, 156.36°W, the most suitable sites are primarily distributed in the marginal areas, and problematic areas are eliminated.

3.4. Route Analysis of Selected Potential Landing Sites

China aims to conduct in situ measurements in the PSR as part of the CE-7 Mission. A lunar lander carrying a mini-flyer will arrive at the sun-illuminated region (SIR) to provide solar power. Figure 18b shows the schematic diagram. To verify the reliability of the potential points, we select the de Gerlache crater for site selection and perform planning of the landing site based on the CE-7 mission requirements using the proposed approach in this paper.

For the de Gerlache Crater, we choose two elliptical landing zones, L1 and L2, and analyze two routes for each, L1−S1, L1−S2, L2−S3, and L2−S4. Figure 17a shows that the flight distances of L1 in S1, and S2 for exploring the shadowed area are 1.9 km and 4.9 km, respectively, where S1 is at 88.04°S, 85.30°W, and S2 is at 88.15°S, 86.02°W. The flight distances of L2 are also 4.2 km, and 6.5 km, respectively, with S3 located at 88.11°S, 80.78°W and S4 at 88.23°S, 79.92°W. We also analyze L2−S3 and L2−S4 to explore the presence of water ice. Figure 18b shows the LROC NAC image indicating the flight path of CE-7. Figure 19c,d are the slope analysis diagrams for L2, S3, and S4, respectively, where the resolution is 20 m. For L2−S3, the mini-flyer can reach the sampling sites for which the detailed analysis is shown in Figure 19.

Figure 19a illustrates the altitude and slope of the L1 to S1 flight path. It is seen that the horizontal and vertical paths are about 1.9 km, and 150 m, respectively. The short path facilitates water ice exploration within a short distance. Figure 18b shows that the average maximum temperature in the L1 region is around 190 K. Nevertheless, the illumination intensity in almost 12% of the L1 region (about 1.3 km distant) is located inside the lunar shadow region, hence solar charging needs to be considered.

Another flight path is from L2 to S3 in de Gerlache (Figure 18c). The area is flat around L2 and S3. Around 35% of the L2 region has a high temperature and sufficient light intensity in the region closer to the PSR, the temperature is, however, lower at around 100 K. The horizontal and vertical travel distances are about 4.3 km and 650 m, respectively. The driving route of the lander needs to be further investigated.

4. Conclusions

Identification of the Moon/Mars landing sites is a multifaceted problem determined by many factors. This paper presented systematic analyses of the landing engineering constraints and quantified their impacts. A fuzzy cognition and selection model was then established and applied to two candidate landing zones for lunar south pole missions. The proposed method can be extended to quantitative evaluation of alternative landing zones for the Moon and Mars missions, considering multiple engineering constraints.

We considered the lunar south pole as the focus of the future CE-7 mission. We analyzed the landing zones’ parameters, including their terrain, temperatures, illumination intensities, and other environmental factors affecting the planning of the landing mission. Using an iterative analysis of these parameters, we then quantified their degree of importance. Using fuzzy cognition, we then filtered out the regions that do not meet the mission requirements. The landing zones in the region above 80°S in the lunar south pole were then selected according to the engineering constraints and mission requirements. The regions meeting the mission requirements are mainly distributed in the de Gerlache (88.48°S, 88.34°W) and Shackleton (89.796°S, 54.9375°E) craters. We verified flight paths for exploration from the landing area to the PSRs for these preselected landing areas. We found that the flyby probe could accomplish the exploration mission under the constraints, further determining the feasibility of the alternative area. The proposed method can be also used to quantitatively evaluate alternative landing areas for other missions subject to a range of engineering constraints and mission requirements. Note that the availability of higher resolution DEM and image data improves the accuracy of path planning in our proposed analysis. This study also shows that there is more than one scenario for exploring the lunar south pole.