We used images taken by the Lunar Reconnaissance Orbiter (LRO) Narrow Angle Camera (NAC) (Robinson, 2010; Robinson et al., 2010; Speyerer et al., 2012; Humm et al., 2016; Mahanti et al., 2016) to quantify the availability of boulders at the two sites of interest. The NAC images were obtained as EDR (Experimental Data Record) and processed using ISIS3 (Laura et al., 2023) to derive georeferenced images, following Bickel et al. (2021). The mapping of the boulders then was done using QGIS ² version 2.18.28. Some minor processing steps of the resulting shapefiles were done with Python and GDAL (GDAL/OGR contributors, 2020).

The two NACs have a nominal resolution of 0.5 ^m/_pixel at an altitude of 50 km, enabling the detection of “blocks” with horizontal sizes of about 1 m (Robinson et al., 2010). The size of most boulders in the images is only a few pixels. Similar as done by Boazman et al. (2022), only boulders which are at least two pixels wide were mapped. Boulders can be identified by their bright appearance followed by a shadow, while the order of bright and dark pixels is opposite to how it is the case for craters (Gawronska et al., 2020; Boazman et al., 2022).

For Connecting Ridge, we utilized shapefiles provided by Boazman et al. (2022) featuring the location of boulders in this region. With the help of this data, we generated boulder shapefiles, which additionally have information on the size of the boulders. A list of the NAC images used by Boazman et al. (2022) is given at the end of their paper. Our augmented boulder shapefiles are available online (Walther et al., 2023).

For the chosen region at the Aristarchus Plateau, no files with mapped boulders were available. Therefore, the whole mapping process was done for this region, starting with the selection of NAC images that were used. The NAC images were chosen with help of the QuickMap ³ , with the goal of getting the best visibility for boulders, e.g., using images with high resolution and intermediate solar incidence angle. Regions that were covered by multiple images were mapped with the image with highest resolution. We note that there is a high variation in the resolution of the available images, which affects the size of the smallest identified boulders. The southern part of the chosen region contains parts of the Vallis Schröteri. Here, we consider a traverse of the rille’s slopes ( > 25°) to be infeasible, which is why the area was excluded from boulder mapping.

We combine our mapping results with boulder size-frequency distribution laws to estimate the fraction of boulders smaller than ∼2 m. Li et al. (2017) used a power law α ⋅ d ^β to derive the cumulative number of lunar boulders of a certain size d or larger. They compared the data with surface and NAC images in a log-log plot and found out that, except for two of the seven considered landing sites, the data points resulting from the two different imaging methods had the same slope. Based on that they claim that the size-frequency distribution (SFD) of the boulders on the Moon can be modeled using a power law. The SLS-SPEC-159 Cross-Program Design Specification for Natural Environments (DSNE) (NASA, 2021b) also assumes that a power law would be valid for rocks smaller than 2 m (see section 3.4.1.4 in the mentioned document). Baloga et al. (2012) on the other hand stated that a power law leads to unreasonable extrapolations for lunar boulders with size 10 cm, while an exponential law α ⋅ exp (βd) does not have this issue. Rüsch et al. (2022) find that the size-frequency distribution of lunar boulders depends on the age of the considered location. They state that the size-frequency distribution of regions younger than approximately 50 Ma is a power law, while for older regions, it is an exponential law.

Due to different views in literature and as the age of the considered regions are not exactly known and also are assumed to vary within the regions, both the power law (Li et al., 2017) and the exponential law (Rüsch et al., 2022) will be considered in the following. We note that the exponential law is more conservative with respect to the estimated amount of small boulders. This will further be discussed in section 5.3.2.

The size-frequency distribution laws are fitted using the data of the boulders that were mapped as described in section 3.1. For the size d in the size-frequency distribution laws, the longest visible axis of the boulders was used. For the power law, the power index β is region-dependent (Krishna and Kumar, 2016; Rüsch et al., 2022). It therefore should not be assumed to be constant over the whole region. Based on that, it can also be assumed that the size-frequency distribution can be regionally dependent, when the exponential law is used instead.

The fit of the exponential law is derived by applying the natural logarithm and then solving the linear system of equations for ln α and for β. For the power law, a maximum likelihood approach was used, which was proposed by DeSouza et al. (2015) for size-frequency distributions in the context of celestial bodies, which in turn was based on Clauset et al. (2009) and therefore also on Muniruzzaman (1957). A threshold d _threshold for the minimum size of the boulders used for the fit was set. This was done for both mentioned size-frequency distribution laws. The used value was 2 m and motivated by Powell et al. (2023). Fits of the power law and the exponential law for the mapped boulders in Connecting Ridge and the chosen Aristarchus Plateau region will later be shown in the discussion in section 5.3.2.

The precise volume of the mapped boulders is unknown, and thus an approximation based on the longest diameter is performed. We introduce a factor, which relates the cube of the longest diameter d _long to the estimated volume of the boulder V _b . The volume estimate is done by assuming the boulder to be an ellipsoid, as applied by Bickel et al. (2021). It can be assumed, that the height of the boulder corresponds to the smallest of the three axes (Demidov and Basilevsky, 2014). Using a ratio between the height and the visible diameter in surface made images, which was mentioned to be 0.6 by Demidov and Basilevsky (2014), together with an approach mentioned by them to relate this visible diameter with the longest and medium axis length, and by using a ratio between the longest and medium axis length of 2, which is the most conservative value mentioned by Krishna and Kumar (2016), the following relation can be obtained (used for this study) V b ≈ 0.1 ⋅ d long 3 (1)

Our standard assumption is that the useable boulders for the construction are those with the longest axis d _long being in the interval [0.5 m, 1.5 m]. Given a map with large boulders mapped using LRO NAC images, the number of small boulders in a certain area can be estimated based on a size-frequency distribution law from section 3.2. While the map with large boulders contains the location of the boulders, the exact location of the expected smaller boulders of course is unknown. Therefore, a map with smaller boulders should rather be a grid, in which for every grid cell, a separate size-frequency distribution is fitted, which allows to get the number of small boulders. The standard value for the grid spacing was chosen to be 200 m. Choosing it much smaller would not make sense due to the uncertainty of the position of the NAC images, which leads to an uncertainty of the position of the mapped boulders.

As mentioned in section 3.2, the size-frequency distribution is region-dependent (Krishna and Kumar, 2016; Rüsch et al., 2022). Both parameters, so not only the scaling α, but also β, which stands for the ratio between large and small boulders, therefore should be estimated for all grid cells individually. For the fit of β, a minimum number of 400 close-by boulders was used in order to get a good sense of the ratio between large and small boulders. Given the size-frequency distribution of a grid cell, not only the number of smaller boulders can be estimated, but also the volume of boulders with d _long in the interval [0.5 m, 1.5 m]. For this, the relation between longest axis and the boulder volume as shown in Eq. 1 is used. The exact formulas are also shown in the Supplementary Material.

Manual boulder mapping is a time-consuming process. As an alternative, we propose using rock abundance data (Powell, 2022) derived by Powell et al. (2023) using LRO’s Diviner instrument in combination with a description of the fractional area F(d) of boulders of size d or larger (Li and Wu, 2018) to calculate the locally available boulder volume. Note that the mentioned rock abundance data is only available between the latitudes 70 S and 70 N. The Diviner instrument is able to sense rocks larger than 1–2 m (Bandfield et al., 2011; Powell et al., 2023). The rock abundance data k _diviner needs to be converted to the total rock abundance k before it is used. This can be done by requiring F (1 m) to be equal to k _diviner and solving it for k. Using the value 1 m instead of 2 m is more conservative with respect to the expected amount of available boulders, as it estimates a lower total rock abundance k.

The volume of boulders with d _long in the interval [0.5 m, 1.5 m] then can be calculated (Li and Wu, 2018) (section 3.3). The exact formulas are shown in the Supplementary Material. Note that boulder volume maps first are generated with the grid given by the rock abundance data of Powell (2022), and afterwards interpolated to a 200 m by 200 m grid, as a 200 m spaced grid is also used in the method based on mapped boulders.

Figure 3 compares the expected available boulder volume of boulders with longest axis between 0.5 m and 1.5 m in Connecting Ridge, the chosen Aristarchus Plateau region and three of the Constellation Program regions of interest. The different size-frequency distribution laws mentioned in section 3.2 were used, including the exponential law and power law together with mapped boulders and the rock abundance dependent exponential law by Li and Wu (2018). The Connecting Ridge site (exponential law) is shown separately in Figure 4 in large.

In the following, the problem statement of the path planning for the collection of the boulders is described. The goal of the path planning was to minimize the overall boulder collection distance. This size is linear to the required time and furthermore also has an influence on the total energy consumption, as will be described in section 4.4 and section 4.5.

The path planning pipeline consists of multiple modules. It uses a greedy score, motivated by Walther et al. (2022), which is used to select the next target location for the boulder collection. A global planner then searches for the shortest path to the target using the A* algorithm introduced by Hart et al. (1968). The A* algorithm is an adjusted version of the Dijkstra algorithm (Dijkstra, 1959), which, for example, was used by Pena-Asensio et al. (2023) for the path planning of lunar EVA’s. The distance to collect the boulders at the target site itself then is estimated using a formula proposed by Few (1955). The global path planner additionally ensures the payload capacity constraint of the vehicle by sending it back to the base camp location to unload the boulders, when the payload capacity is about to be reached.

A further module of the path planning pipeline is a local planner, which ensures the slope constraints of the vehicle and keeps it out of permanently shadowed regions. For the slope constraint, the elevation data of Barker et al. (2021) is used for Connecting Ridge and the SLDEM2015 data of Barker et al. (2016) otherwise. Regions are considered to be permanently shadowed if the 60 m spaced Sun visibility data of Mazarico et al. (2011) is equal to zero at the corresponding location. For more details about the implementation of the path planning pipeline, the interested reader is referred to the Supplementary Material.

This section presents the results of the boulder collection distances using the path planning pipeline described in the previous sections. The considered task thereby is to collect 250 m³ of boulders, which is about enough for a quarter ring segment of a blast shield as mentioned in section 2. The results are shown in the form of distance maps, where the color of a pixel indicates the collection distance required to build a quarter ring segment at that particular location. Black pixels denote sites without access to a sufficient amount of boulders, as otherwise the slope constraints of the vehicle would be violated or permanently shadowed regions would be entered.

Figure 5 shows the distance map of Connecting Ridge by using an exponential law for the SFD. Note that the x- and y-axis are the position in [km] in the polar-stereographic coordinate system. Figure 6 compares the collection distance maps with different regions and with different size-frequency distribution laws for the boulders. For Connecting Ridge, the x- and y-axes are the polar-stereographic x- and y-coordinates. For the other regions, the x- and y-axes are x- and y-coordinates of a flattened coordinate system with origin in the center of the respective region.

The overall time for the construction, assuming the boulder collection and the construction itself take part sequentially, is composed as: t total = t collect,driving + t construct,driving + t handling , (2)

where t _{collect, driving} is the needed time for driving to collect the required boulders, t _{construct, driving} the time for driving during the construction and t _handling the time to scan and place the boulders.

For the calculation of the driving times, the velocity of the LRV of the Apollo missions is taken as a reference. For the Apollo 15 mission, the average velocity was 9.2 ^km/_h according to Jones and Nola (1971). The calculation of the handling time is based on the value 21 ^min/_stone by Johns et al. (2023). The exact formulas are shown in the Supplementary Material.

Note that the time calculated as in Eq. 2 is the operational time and neglects charging times and furthermore also the lunar nights, during which operation might not be feasible. The actual time therefore might be about twice as long.

The overall energy for the construction is E total = E collect + E construct , (3)

where E _collect is the needed energy to collect the required boulders and E _construct the energy for the construction itself.

E _collect and E _construct furthermore are composed of the work against the driving resistance and the work related to the potential energy change during the collection: E collect = W collect,driving + W collect,pot (4) E construct = W construct,driving + W construct,pot (5)

The calculation of the individual parts is shown in the Supplementary Material. Some of the calculations require the gravitational constant of the Moon g _M and the density of the boulders ρ _b . For this, the values g _M = 1.64 m/s² and ρ _b = 2650 kg/m³ provided by Susante and Metzger (2016) are used. Note that W _collect,pot also can be negative. We use the elevation data by Barker et al. (2021) for the Connecting Ridge site and the SLDEM2015 data by Barker et al. (2016) for the Aristarchus site.

We assume the driving work to scale linearly with distance and mass, which accords with a formula by Sripad and Viswanathan (2017). The energy per distance and mass is estimated based on data of the LRV of the Apollo missions, which was mentioned by Jones and Nola (1971) and results in 0.334 J/m kg.

The vehicle mass m _vehicle is also approximated using data of the LRV given by Jones and Nola (1971), which is scaled according to the payload capacity. For the mass of the incorporated excavator, a rough estimate was done based on a data sheet ⁵ of Menzi Muck. For the full formula of the vehicle mass, the interested reader is referred to the Supplementary Material.

We use some of the parameters of Table 1 to compute the median values of the boulder collection distance and different energy and time components of all base camp sites in Connecting Ridge for a quarter segment of a blast shield (Table 2). An exponential law (boulder size frequency distribution) was assumed when generating those results.

Furthermore, we present the results of a specifically chosen base camp site in the middle of Connecting Ridge. This base camp site was selected based on the local slope (motivated based on the HLS requirement HLS-S-R-0022 (NASA, 2022a)), in direct proximity of the ridge’s topographic summit, maximizing illumination and direct-to-Earth communication (NASA, 2022c). For this, we used elevation data of Barker et al. (2021) and Sun and Earth visibility data of Mazarico et al. (2011). We again consider a quarter segment of a blast shield, use parameters of Table 1 and assume an exponential law (boulder size-frequency distribution). The resulting boulder collection distance, as well as the energy and time components for this selected base camp site are summarized in Table 3. The driving work turns out to be larger than the energy related to the potential energy change of the collected boulders. The latter one, however, is also not negligible, which is due to the fact that the chosen base camp site is located in a topographic high, as can be seen in elevation data of Barker et al. (2021). The required energy for construction turns out to be much lower than the required energy for the collection of the boulders.

The resulting path to collect the boulders is visualized in Figure 7. The white square with black edge in Figure 7 shows where the base camp site and the landing site of the excavator are located. As the base camp site fulfils the excavator landing site requirements mentioned in section 4.1.3, the two sites are identical. The right map in the figure indicates sites with available boulders. The vehicle has to traverse a significant portion of the area to collect the boulders, focusing on target locations with high boulder abundance.

In Figure 3, the boulder volume maps of different regions and via different assumptions on the size-frequency distribution law were compared. Boulder volume maps based on manually mapped boulders tend to be sparser than maps based on rock abundance data, which rarely feature locations without boulders. There is also a difference between the resulting expected boulder volume as derived with a power law and an exponential law (both with manually mapped boulder data), which will further be discussed in section 5.3.2.

We note that in case the available boulder volume is insufficient, the region where boulders are collected could simply be enlarged. Furthermore, the Moon is known to have subsurface rocks (Thompson et al., 1970; Elder et al., 2019). As an alternative, those subsurface rocks could be dug out and used for construction. Potential disadvantages include dust ejection and an increased energy consumption (Taylor et al., 2005; Lim et al., 2017).

This section shows multiple trade-offs between design parameters and their implications on the proposed construction method.

This section shows the influence of uncertainties on the results. Note that the trade-offs in section 5.2 in contrast were showing the influence of design parameters on the results.

The proposed construction method is facing a series of challenges, some of which require further consideration. A dry stone wall constructed using irregular, unprocessed boulders will contain small gaps. It needs to be examined, whether those gaps are an issue when the wall is used as a blast shield. This will require simulations and experiments under lunar conditions. In case the regolith blasts could pass through the gaps, it would be necessary to seal them, e.g., by using small boulders or loose regolith.

A further challenge is the travel distance and time required to collect the material and construct a blast shield. As shown in Figure 5, the distance to collect the boulders can be around 1000 km. Table 2 on the other hand showed, that the median operation time is about 1500 h, which corresponds to 63 full Earth days. This does not include charging times or hibernation during the lunar night, which is why the actual mission time will be at least twice as long. As a reference, the Lunokhod 1 rover was operative for 321 Earth days and travelled ∼10 km (Karachevtseva et al., 2013). This indicates, that the mission duration is achievable. The LRV of the Apollo 17 mission on the other hand drove approximately 35 km in about 4.5 h driving time Smith et al. (1973), which shows, that much farther distances than the mentioned one of Lunokhod 1 are possible—assuming the rover can reach a human level of navigation autonomy. A remaining challenge will be the recharging process. The robotic excavator thereby might either harvest energy by itself, rely on a few recharging stations, or could be powered by RTGs (radioisotope thermoelectric generators).

In the following, the energy consumption of two alternative blast shield construction methods are calculated and compared to the energy consumption of the proposed method. We note that the creation of un-cast regolith berms, as proposed by Mueller et al. (2009) and Moses and Mueller (2021), is not discussed here. This method probably would need less energy than the other construction methods, but comes with other disadvantages: the impacting stream of spacecraft exhaust and pebbles/dust could erode a regolith berm over time (Morris, 2012). In addition, the excavation and dumping of large amounts of regolith can lead to serious issues with the resulting dust (Taylor et al., 2005; Lim et al., 2017).

Figure 7 suggests that the collection of boulders can be quite invasive, as boulders are systematically moved across the surface, negatively impacting future scientific studies. The sustainable utilization of lunar resources—including boulders—is subject to an ongoing debate (Pirtle et al., 2023). We note that the systematic collection of boulders might in fact aid scientific analyses, if properly conducted: all boulders remain unprocessed and can be accessed in the blast shield wall (Johns et al., 2020). Context data collected before and during the collection of boulders (location, orientation, composition, etc.) could be used to create a digital twin of the area of interest, opening up new research venues, such as related to the regional study of impact ejecta composition.

In future missions to Mars, ISRU will become even more important, as the transportation costs from Earth to Mars are much higher than from Earth to the Moon, due to the larger distance, motivating a basic comparison of the median available boulder volume on the Moon and on Mars. For the Moon, the rock abundance dependent exponential law by Li and Wu (2018) and the rock abundance data of Powell (2022) and Powell et al. (2023) was used. For Mars, the rock abundance dependent exponential law and boulder axis length ratio by Golombek and Rapp (1997) and information about the rock abundance of Christensen (1986) was used. For the lunar case, the median area that contains 250 m³ of boulders is slightly larger than 0.2 km ² , while the median area on Mars that contains 250 m³ of boulders is about 0.06 km ² . This shows, that the proposed construction method would work even better on Mars than on the Moon. We note that the regional geologic context can significantly influence the availability of boulders, particularly on an atmospheric planet like Mars.

This section gives an overview of what work remains open for future research. As mentioned, the estimate of the available amount of boulders has some uncertainties. High resolution images of landers at the regions of interest will allow to get a better understanding of how many small boulders are available. Furthermore, the usage of the proposed construction method could be expanded to also build arch vaults, which could be used as habitats and shelters. The capability of autonomously constructing arches with irregular boulders will need to be demonstrated in experiments. Finally, an excavator capable of operating in the lunar environment needs to be developed and the exact dimensions of the infrastructure need to be set.