Acta Astronautica 214 (2024) 324–342 Contents lists available at ScienceDirect Acta Astronautica journal homepage: www.elsevier.com/locate/actaastro Automated astronaut traverses with minimum metabolic workload: Accessing permanently shadowed regions near the lunar south pole Eloy Peña-Asensio a, b, *, Jennifer Sutherland c, d, Prateek Tripathi e, Kashauna Mason f, Arthur Goodwin g, Valentin T. Bickel h, David A. Kring i a Departament de Química, Universitat Autònoma de Barcelona, Bellaterra, Catalonia, 08193, Spain b Institut de Ciències de l’Espai (ICE, CSIC), Campus UAB, C/ de Can Magrans S/N, 08193, Cerdanyola del Vallès, Catalonia, Spain c Institut Laue-Langevin, 71 Av. des Martyrs, 38000, Grenoble, France d Institute of Aeronautics and Astronautics, Technische Universität Berlin, Marchstr. 12-14, 10587, Berlin, Germany e Department of Civil Engineering, Indian Institute of Technology, Roorkee, Uttarakhand, 247667, India f Department of Geology and Geophysics, Texas A&M University, 400 Bizzell St., College Station, TX, 77843, USA g Department of Earth and Environmental Sciences, The University of Manchester, Oxford Rd., Manchester, M13 9PL, United Kingdom h Center for Space and Habitability, University of Bern, Gesellschaftsstr. 6, 3012, Bern, Switzerland i Lunar and Planetary Institute, Universities Space Research Association, 3600 Bay Area Blvd., Houston, TX, 77058, USA A R T I C L E I N F O A B S T R A C T Keywords: The Artemis exploration zone is a topographically complex impact-cratered terrain. Steep undulating slopes pose Artemis a challenge for walking extravehicular activities (EVAs) anticipated for the Artemis III and subsequent missions. Permanently shadowed regions Using 5 m/pixel Lunar Orbiter Laser Altimeter (LOLA) measurements of the surface, an automated Python Lunar south pole pipeline was developed to calculate traverse paths that minimize metabolic workload. The tool combines a Astronaut Monte Carlo method with a minimum-cost path algorithm that assesses cumulative slope over distances between a lander and stations, as well as between stations. To illustrate the functionality of the tool, optimized paths to permanently shadowed regions (PSRs) are calculated around potential landing sites 001, nearby location 001(6), and 004, all within the Artemis III ‘Connecting Ridge’ candidate landing region. We identified 521 PSRs and computed (1) traverse paths to accessible PSRs within 2 km of the landing sites, and (2) optimized descents from host crater rims into each PSR. Slopes are limited to 15◦ and previously identified boulders are avoided. Surface temperature, astronaut body illumination, regolith bearing capacity, and astronaut-to-lander direct view are simultaneously evaluated. Travel times are estimated using Apollo 12 and 14 walking EVA data. A total of 20 and 19 PSRs are accessible from sites 001 and 001(6), respectively, four of which maintain slopes <10◦ . Site 004 provides access to 11 PSRs, albeit with higher EVA workloads. From the crater rims, 94 % of PSRs can be accessed. All round-trip traverses from potential landing sites can be performed in under 2 h with a constant walk. Traverses and descents to PSRs are compiled in an atlas to support Artemis mission planning. 1. Introduction permanently shadowed regions (PSRs). As noted decades ago [6], these regions are very cold (<120 K) and may trap volatile material like water The initial Artemis exploration zone (AEZ) is a region within six ice. Such areas could provide another resource for sustained develop­ degrees latitude of the lunar south pole (Fig. 1). The Sun circumnavi­ ment of the lunar surface; water can be used for crew consumables, gates this region near the horizon, providing near-constant illumination radiation shielding, and rocket propellant. Captured volatiles also offer to the highest summits [1–3]. Several of these locations were identified important information about the origin, delivery, and evolution of vol­ as potential Artemis landing sites [4], in part because solar power can be atile substances in the Earth-Moon system. In a study commissioned by used to support a sustainable presence. NASA, the National Research Council (2007) [7] recommended in­ As the Sun is within a few degrees of the horizon, the topography of vestigations for future crewed and robotic missions to (a) determine the the impact-cratered terrain casts long shadows. Some areas are compositional state and distribution of the lunar volatile component, (b) * Corresponding author. Departament de Química, Universitat Autònoma de Barcelona, Bellaterra, Catalonia, 08193, Spain E-mail addresses: eloy.peas@gmail.com, eloy.pena@uab.cat (E. Peña-Asensio). https://doi.org/10.1016/j.actaastro.2023.10.010 Received 8 May 2023; Received in revised form 21 August 2023; Accepted 10 October 2023 Available online 14 October 2023 0094-5765/© 2023 The Authors. Published by Elsevier Ltd on behalf of IAA. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 1. Upper left: past crewed surface missions were limited to equatorial latitudes. Middle: Principal craters within the AEZ; the blue rectangle straddling Shackleton crater delineates the considered region of interest. Upper right: topography overlaid on LOLA hillshade (5 m/pixel); black polygons indicate a LOLA illumination data-derived PSR product of four pixels or more (60 m/pixel) [2], while inset red polygons are landing zones that meet Artemis III Human Landing System slope requirements [5]. Data credits: NASA/LROC/GSFC/ASU. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) determine the sources of lunar polar volatiles, (c) understand the identified as suitable for the Artemis III Human Landing System’s (HLS) transport, retention, alteration, and loss processes experienced by vol­ requirements for a surface with a slope <8◦ , that are at least 100 m from atile materials in lunar PSRs, (d) understand the physical properties of steeper slopes [5]. Among those seven areas, the largest is designated the extremely cold polar regolith, and (e) determine what the cold polar 001(6). Site 004 is on the rim of Shackleton crater. Sites 001, 001(6), regolith reveals about the ancient solar environment. These targets are and 004 are used here to define a region of interest (ROI) 18.5 × 16.2 km incorporated in the Artemis III science objectives as a series of Goal 2 (~300 km2) (Fig. 1). investigations [4]. That ROI contains several types of geologic targets [8–12] that as­ Those PSRs, and all proposed Artemis III candidate landing regions, tronauts can explore to illuminate the history of the Moon, its neighbor occur within a feldspathic highland terrain that provides opportunities Earth, and the inner Solar System, while also evaluating the distribution to address many other NRC (2007) exploration science objectives, i.e., to of icy resources [4,7]. To illustrate the application of our EVA planning evaluate the bombardment history of the inner solar system; to sample a tool we focus on PSR targets, first mapping PSR locations within the diverse suite of lunar crustal rocks; to study impact processes; and to region and then applying the tool to calculate EVA routes that minimize study regolith processes [7]. metabolic workload. While we demonstrate how the tool can be used to A key to mission success will be accessing promising stations iden­ optimize astronaut traverses to PSRs, it can be applied to any other tified in pre-mission mapping. Owing to locally heterogeneous slopes, geologic and exploration targets. large elevation changes, and low illumination, extravehicular activities (EVAs) may be challenging. Automating the initial assessment of a large 2. Geologic context number of potential targets can benefit the planning of these traverses. To filter the abundance of opportunities and more efficiently design The lunar south polar region is an impact-cratered surface super­ routes, we developed a computational mapping tool for calculating imposed on the rim of the Moon’s largest impact basin, the South Pole- traverse paths that minimizes the metabolic workload on crew. We Aitken (SPA) basin [13]. The SPA basin-forming event, estimated at 4.25 demonstrate its utility by applying to the Artemis III candidate landing to 4.39 Ga [14–16], generated a series of massifs along its margin, some region ‘Connecting Ridge’ and potential landing sites therein. of which have such high unobstructed elevations >1800 m that they are Potential landing site 001 is along the ridge between Shackleton and exposed to sunlight up to ~85 % of the time [1–3,17]. Although pri­ Henson craters [2,4]. In the vicinity of site 001, seven polygons were marily feldspathic highland terrain, redistributed material excavated 325 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 2. Interpreted cross-section of the ‘Connecting Ridge’ (center left) and Shackleton crater. Shackleton impact ejecta blankets the ridge. Drawing upon the Apollo 16 landing site, which also occurred in a feldspathic terrain, one infers a series of lithologies (pictured) might be found in proximity to the ‘Connecting Ridge’. Elevation and distances extracted from LOLA and NAC data. Photographs courtesy of LPI Lunar Sample Atlas and Washington University in St. Louis; section developed from Ref. [11]; SPA basin profile from Ref. [25]. from depths of 100 km during the impact [18] may also include con­ lithologies within the PSR are assumed from a standard model of crater tributions from the entire crustal column of anorthosite, troctolite, formation and simulation efforts [10,26–29]. The chemical and isotopic norite, and gabbro, plus upper mantle lithologies [19,20]. compositions of crustal lithologies exposed near the lunar south pole (e. A series of pre-Nectarian (e.g., Haworth, 4.18 ± 0.02 Ga; Shoemaker, g., anorthosite, norite, troctolite) may contribute to further developing 4.15 ± 0.02 Ga; Faustini, 4.10 ± 0.03 Ga), Nectarian (e.g., de Gerlache, the lunar magma ocean hypothesis [7], and their diversity could help 3.9 ± 0.1 Ga), and Imbrian (e.g., Slater, 3.8 ± 0.1 Ga; Sverdrup, 3.8 ± illuminate the evolution of the lunar crust far from the Apollo sites. 0.1 Ga) age impact craters [21,22] further reworked those lithological Impact melts along the ridge could span the range from that of the SPA components. basin to Shackleton impact events, providing an opportunity to better Shackleton crater was the last major impact shaping the region. It has constrain the age of the oldest basin-forming impact on the Moon, to test an estimated age of 3.43+0.04 − 0.05 Ga from crater counting [23]. This ~21 km the lunar cataclysm hypothesis, and assess the orbitally-determined age diameter by ~4.1 km deep feature excavated two lithological units: a of Shackleton to help calibrate lunar crater chronology. massif composed, in part, of anorthosite, overlain by at least one strat­ Those cratering processes produced the irregular surface of the AEZ, ified unit exposed on the crater wall that likely represents successive including depressions that host PSRs. Over geologic time, water and ejecta blankets [11]. other volatiles transported to the poles may have been trapped in PSRs. The Artemis III ‘Connecting Ridge’ candidate landing area is blan­ The largest deposits of water ice could have been delivered by the oldest keted by Shackleton impact ejecta that may be ~150 m thick on the rim crater-forming events and incorporated within their ejecta blankets, [10], thinning with distance along the ridge (Fig. 2). Orbital spectros­ then buried by subsequent ejecta [30,31]. Smaller PSRs accessible via copy at a spatial resolution of 1 km/pixel indicates the region is domi­ walking EVAs will have been produced by younger (<100 million years nated by plagioclase [11], with the lowest FeO values (~8–16 wt%) in old) cratering processes. Any ices within those PSRs will likely be the AEZ found in the area around Shackleton crater (including sites 001 dominated by volatiles delivered by solar wind and impacting and 004) [11,24]. These FeO values are consistent with small amounts of micrometeorites. mafic minerals that are normally co-mingled with anorthosite but may also represent a contribution from SPA impact melt in the regolith 3. Data and methods covering the ridge. Because the terrain encompassed by the AEZ is similar to, albeit 3.1. Path-finder algorithm much older than, the feldspathic material of the Apollo 16 site, we infer astronauts may traverse (and collect) a surface composed of anorthositic Route design for EVAs has typically been completed manually by regolith breccias, fragmental breccias, impact melt breccias, and soils geology experts. Owing to recent lunar orbital missions, topographic (Fig. 2), dotted with a large number of boulders [8]. Obscured data is now available at high resolution (up to 5 m/pixel) for elevation 326 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 and slope. This accuracy allows the implementation of minimum-cost same time, it also evaluates bearing capacity, temperature, astronaut calculation algorithms to obtain optimized traverses that reduce both sunlight incidence (for a given date), traverse walking time, and distance traveled and the risk from high slopes. Particularly in the astronaut-to-lander view opportunity. context of rover routing design, several efforts have been made to develop algorithms that find the optimal path between two points on a 3.2. Processing pipeline map. Graph theory offers a solution to find the shortest path between nodes in a network, which, for practical purposes, is defined as the raster The data processing pipeline requires a series of baseline data pixels that comprise a map. We briefly review the main alternatives and products, which we developed using primary and secondary Lunar highlight the relative strengths of the adopted Dijkstra solution. Reconnaissance Orbiter (LRO) data products. The topography of the The method developed by Ref. [32] incorporates human intervention region is assembled using an enhanced 5 m/pixel LOLA data product to fine-tune the path and ensure compliance with mission rules, where [46] derived from LOLA Digital Elevation Counts (LDEC), a LOLA Digital small adjustments could have led to improved traverses, such as Elevation Model (LDEM), and a LOLA Digital Slope Model (LDSM). The avoiding violations of the metabolic cost constraint and enhancing vis­ published geolocation uncertainty is ~10–20 cm horizontally and ~2–4 ibility and sun score. They note that estimating a low-energy direction of cm vertically for each pixel. Note, however, that ~90 % of the 5 travel mode is possible through the use of the directional height-height m/pixels are interpolated, i.e., do not contain physically measured data. correlation function [33]. However, this approach does not explicitly For visual inspection of the region and to obtain detailed images of search for the minimum-cost path between two points by evaluating all the PSRs, we use a 1 m/pixel mosaic of the south polar region [47] which possibilities in an efficient manner like Dijkstra’s algorithm [34]. was generated from the 0.5 m/pixel Lunar Reconnaissance Orbiter When planning in high-dimensional and dynamic environments, (LRO) Narrow Angle Camera (NAC) data [48], orthorectified using a 5 stochastic algorithms are commonly used. One such approach is random m/pixel DEM and registered horizontally to the LOLA global DEM [49]. sampling-based planners, such as probabilistic roadmaps (PRMs) [35] An assemblage of NAC images downloaded and calibrated using Inte­ and rapidly-exploring random trees (RRTs) [36], which work by sam­ grated Software for Imagers and Spectrometers (ISIS) was also mosaiced pling a probabilistic graph to find a path to the goal [37]. developed a to create base maps. The data was georeferenced and mosaiced using variant of RRTs, known as RRT*, that finds asymptotically optimal paths ENVI and ArcGIS 10.6 software [50]. by updating edge connections. However, sampling-based planners can To determine the mean bolometric brightness temperatures, ~10 generate poor paths if many suboptimal or undesirable states are years of nadir-pointing Diviner Radiometer Experiment observations sampled, especially when computation is limited. RRTs build a tree were compiled [51] from 7 IR channels over a wavelength range of 7.55 structure by randomly sampling points in the search space and con­ μm–400 μm. For the present study, we use the Level 4 gridded 240 necting them to the nearest point in the tree. They are probabilistically m/pixel Polar Cumulative Products described in Ref. [52], focused on complete, meaning a solution will eventually be found if one exists, but the southern summer season as indicative of minimum PSR extent and there is no guarantee that it will be optimal. In contrast, Dijkstra’s al­ for more favorable exploration conditions at high latitude. gorithm is a complete algorithm: it is guaranteed to find the shortest A bearing capacity map with 5 m/pixel resolution was produced path between two points if one exists, although this can be computa­ following [53] and a variation of Hansen’s formula. Because an analysis tionally expensive when applied to high-dimensional or complex of Apollo and Lunokhod data recommended bearing capacities of >7 environments. kNm− 2 [54], calculated traverses are subsequently restricted to those Using a heuristic, the graph path search algorithm A* [37–39] finds a surfaces. specific start location to the goal in a similar way to Dijkstra’s algorithm. An analysis of Apollo walking EVA speeds [55] was expanded with a However, A* requires more memory space, as it stores all generated new non-linear analysis using transcripts of Apollo 12 (EVA 2) and nodes and depends on the quality of the heuristic function, which can Apollo 14 (EVA 2) traverses [56]. Of these two missions, the latter affect its performance and optimality. covered terrain more akin to upcoming surfaces and astronauts also Field D* [40] is a variant of D*, an informed incremental search hauled a Modular Equipment Transporter (MET), analogous to the tool algorithm [41] that uses linear interpolation to generate smoother paths cart/carrier being designed for Artemis III. in non-uniform cost environments. Field D* is incremental, such that it The locations of PSRs were mapped by applying a process similar to can reuse previous calculations when the environment changes, whereas that of [2], who use 240 m/pixel LOLA data, albeit with the 5 m/pixel Dijkstra’s algorithm has to recompute everything from scratch. As we LOLA equivalent and the simplification of not considering backscattered did not consider a dynamic environment, nor real-time updating of (secondary or reflected) illumination. The process is also comparable to obstacles or changes in topography, we did not implement D* family that of [1,57], though we do not consider the length of time of illumi­ algorithms. nation nor ray tracing, respectively. Candidate PSRs were generated For simplicity, and because EVAs during Artemis III will be limited to using the ArcGIS ’Hillshade’ function on the 5 m/pixel LDEM product. 6 ± 2 h [42], we have considered a fixed temporal lighting condition for The simulated Sun was varied around 360◦ azimuth in 0.5◦ increments a given date, as opposed to other energy budget-aware approaches [3, at a maximum elevation of 2◦ above the horizon, a suitable average for 43–45]. our region as deduced using NASA JPL’s Moon Trek Sun Angle and JPL Considering these different approaches and techniques, we selected Horizons [58,59]. The resultant illumination map was thresholded and Dijkstra’s algorithm as the proper solution for computing traverses that filtered for areas of zero illumination. We then applied four filters. First, minimize the metabolic workload for a specified illumination condition. two automated methods: (1) removing small noisy PSRs <3 pixels in We establish our criterion for minimum metabolic workload based on size, and (2) removing small poorly defined PSRs with <3 LOLA LDEC the assumption that the traverses will be utilized for round trips, with points inside them. The remaining PSRs were manually inspected and each EVA involving visiting a single target. Therefore, our priority is to (3) compared with the 1 m/pixel NAC image mosaic, removing candi­ identify paths that strike a balance between minimizing the accumu­ dates within illuminated regions, or (4) removed if, when plotting tra­ lated absolute slope and achieving the shortest distance possible. By verses, local sun ephemeris for PSRs indicated illumination in their prioritizing both flat terrains and shorter routes, we aim to optimize centers (as we generate the PSRs with a fixed Sun elevation value, which efficiency while reducing the physical exertion required during the could return incorrect results where this elevation increases). Addi­ traverses. tionally, we also mapped PSRs up to 5◦ solar elevation as this limit is We developed a Python pipeline called MoonPath that, given a more enduring in terms of potential accumulation of trapped volatiles, starting point, a maximum slope, and a distance threshold, automati­ with possibility for greater volumes, or perhaps different characteristics. cally computes all optimized traverses to nearby accessible PSRs. At the On geological timescales, the axial tilt of the Moon — and hence solar 327 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 3. Illustration of the Monte Carlo technique applied to compute the optimal descent from the rim to the center of the PSR. The mesh 3D model is a 5 m/pixel slope map overlying a 5 m/pixel LOLA DEM. Randomly generated starting points are shown as large dots on the crater edge. Colored traverses are used only to distinguish different paths. The larger mesh has 5x vertical exaggeration. illumination at the poles — may have shifted significantly after the minimum size of 3 m for the mapped boulders. However, no specific Cassini State Transition 2.5 Ga [60–62]. information regarding the size of each boulder was collected. Addi­ The 5 m/pixel LDEM used in our study presents inherent limitations, tionally [11], identified within our ROI some of the largest boulders, with approximately 90 % of its raster pixels being interpolated, lacking which measured up to 30 m in diameter. Considering that these are original topographic height measurements [46]. To mitigate the impact expected to be less common, we adopted a representative size of 5 m for of these limitations on the generated PSRs, we assessed the percentage each boulder. By imposing a size of a pixel (i.e., 5 × 5 m) for the boulders area of the LDEC raster within each PSR containing non-interpolated in our analysis, we effectively constrain the potential traverses to avoid elevation data points, ensuring a minimum coverage of 5 % for all these geological features. This restriction is based on the understanding PSRs. PSRs with less than 5 % coverage or fewer than 3 LDEC elevation that traversing over or around boulders can pose challenges to astronaut data points were automatically excluded from the analysis. Additionally, mobility and may impede the efficiency of extravehicular activities. we manually removed PSRs that conflicted with the NAC imagery, We adopt thresholds for (1) encountered slopes being <15◦ , which is specifically targeting those situated in illuminated areas. conservative because 20◦ is considered a permissible limit, and (2) the We used Dijkstra’s algorithm, as justified, to produce a shortest-path farthest distance of any traverse point to the lunar lander being no more tree from the starting point (landing site or crater rim) to the endpoint than 2 km [65]. To obtain a more natural path closer to how an astro­ (PSR edge or center), allowing both lateral and diagonal movements naut would walk, we smoothed the slope map under 5◦ outside craters, between adjacent pixels [63,64]. The 5 m/pixel LDSM data is employed meaning slopes <5◦ are treated as the same value. For the interior of as a cost map, using cumulative slope as the optimization metric. The craters, we did not apply any smoothing. Slopes greater than 15◦ are not ‘best’ traverse is chosen by evaluating the lowest cumulative slope forbidden but highly penalized, as some traverses must pass through a result. The algorithm intrinsically considers distance and height. By few high slope pixels. utilizing the LDSM raster as a cost map, the algorithm rewards shorter First, we calculated the optimal path from the landing site to each of paths with lower slopes, as longer distances with lower slopes or shorter the vertices outlining the edge of the PSR. In this way, we obtain the distances with higher slopes would result in a worse cumulative slope. shortest traverse featuring the lowest cumulative slope to the edge of a Height is considered in the slope (as the cumulative slope is assessed), PSR. We then calculated the optimal path from this edge point to the PSR therefore a greater elevation change over a set distance implies a higher center. In addition, we determined the best descent from any point on slope (worsening the cumulative slope result). Given that the graph is the crater rim to the hosted PSR regardless of the landing site for all PSRs represented as an adjacency matrix, i.e., a regular and gapless structure, in the ROI. This uses the same function described above with an addi­ the algorithm effectively balances the trade-off between distance and tional step, as the optimal initial point of lowest-cost descent is not elevation change, resulting in traverses that minimize the cumulative known beforehand. We performed a Monte Carlo simulation by gener­ slope and, consequently, the metabolic workload. ating equally spaced (20 m) random points on the perimeter of the crater Additionally, we included into our study the locations of isolated to compute the optimized descent from each point. Subsequently, all boulders identified by Ref. [8] in the vicinity of sites 001 and 004. These cumulative slope results (for every rim starting point to every PSR edge) features were manually mapped using high-resolution NAC images at are compared to obtain the best descent. Fig. 3 illustrates the optimized approximately 0.5–2 m resolution. The authors stated that they were descent computation process. Note that not all starting points have a able to identify objects that spanned at least 3 pixels, suggesting a viable path (truncated lines). 328 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 4. Left: An illustrated example of the coastline paradox, where the distance between two points decreases with increasing pixel size. Blue and green lines show two different sample step sizes used for smoothing, with aliasing-like behavior for the poorly optimized step size. Right: Augmented Dickey-Fuller test applied to the polynomial fit deviation of the distance as a function of the pixel step. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 5. Top-left: Elevation map (5 m/pixel) of the ROI with 20 m contours, with potential landing sites 001 and 004 (black crosses) both located in areas of high elevation. Top-right: Slope map generated from 5 m/pixel LDEM, with potential landing sites 001 and 004 both located on areas of low slope. Bottom-left: NAC imagery was mosaiced using maximum illumination of pixels. Black areas correlate with areas of poor illumination and/or permanent shadow. Bottom-right: Bearing capacity map generated using LDSM data. 329 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 6. Temperature maps for the ROI generated using Level 4 gridded 240 m/pixel Polar Cumulative Products from Diviner, covering the lunar southern summer during a 10-year period. Potential landing sites 001 and 004 are labeled. For the astronaut body sunlight incidence calculation (to which we 20 cm intervals up to a modeled astronaut height of 2 m to calculate the will henceforth refer to as astronaut illumination, that is, the body area percentage of the astronaut’s body in sunlight. percentage that is illuminated by direct sunlight), we chose as a case Analogous to the astronaut illumination calculation, we ray-traced study the month of maximum solar elevation (or subsolar latitude) for the direct view of the Space X Artemis III HLS window (40 m high 2025 at landing site 001, i.e., the most favorable month in terms of [67]) from the traverses. For each step we checked the percentage of an general terrain illumination conditions. December is the month of 2025 astronaut’s body (again, from 0 m to 2 m, in 20 cm intervals) in visual when the Sun reaches its highest elevation (2.1◦ on the 16th, for the ROI. contact with the lander. This feature could be of considerable assistance In contrast, on 31 December the Sun elevation is 0.8◦ , representing the to guide astronauts during their EVAs in absence of geolocation systems, worst illumination condition for the most illuminated month of 2025). both for self-guiding and to receive directions from the HLS. However, it The position of the Sun is queried to JPL Horizons ephemerides [66]. We would be impossible to maintain eye contact if the Sun is directly behind select these two days to evaluate the full range of traverse illumination the lander. We also address this Sun view orientation-related problem by properties. computing the angular distance between the astronaut-to-lander line of We estimated when the analyzed illumination conditions will be sight and the Sun position. In this way, 0◦ means that the line of sight repeated up to 2029, meaning the obtained results are also applicable to coincides head-on with the Sun and 180◦ indicates the Sun is directly specific days in subsequent years. Illumination conditions on December behind the view. 16, 2025 will occur again on November 6, 2026, October 26, 2027, and Regarding distance computation, we emphasize a problem derived October 14, 2028, while the Sun position on December 31, 2025 will be from the so-called coastline paradox. The calculated traverse for each the same on October 23, 2026, October 12, 2027, and September 1, PSR does not have a well-defined length, as distance calculations depend 2028. on the pixel size of the map, behaving in this way as a fractal dimension Given that low solar illumination angles cast long shadows, this type issue [68]: the larger the pixel size is on a map, the smaller the computed of calculation becomes significant to assess temperature variations an distance will be (Fig. 4 left). In addition, as the minimum-cost path al­ astronaut may be exposed to. To properly compute the percentage of an gorithm is restricted to lateral and diagonal motion between adjacent astronaut’s body that would be illuminated, we developed a bespoke ray pixels, this motion will differ from performed astronaut paths which are tracing code. Using ephemeris from JPL Horizons, we determined the expected to be more direct and thus shorter. Smoothing is needed to local Sun position for every pixel and ray traced from each pixel to the account for restrictive pixel motions and to remove noisy variations Sun. Sunlight is projected onto the lunar surface to evaluate if the inherent in the slope map that overestimate the expected path length. elevation of the terrain is higher than the ray. If the line of sight is We smooth by sampling traverse pixels at an optimized step-spacing, intersected by topography, the ray is blocked, and the pixel does not which must compromise between small spacing (including noisy path receive direct sunlight from this direction. We repeated the process at motions) and large sample spacing (missing important path 330 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 instance, only 12 lunar minutes elapse (normalizing a lunar day of 29.53 Earth days to 24 h), so solar position relative to a fixed point is assumed constant over the duration of a traverse. Whereas seasonality has little influence on surface temperatures at low to mid-latitudes, the interplay of illumination grazing angles in polar regions with topography exerts a significant influence on surface temperature with the position of the subsolar latitude (Fig. 6). 4.2. Apollo traverse speed By comparing maps of traced traverses to transcripts from Apollo 12 and 14 (both EVA 2) missions, way points were generated that link discrete times with spatial positions for a given astronaut (Figs. 7 and 8). Only way points separated by > 25 m were used to ensure traverse speed calculations encompass periods that were predominantly walking, rather than those involving geological activities at stations or short bursts of speed between points of interest. Apollo 12 (EVA 2) had regular stops, and averages contain the time for geological observations and photographs. Apollo 14 (EVA 2) was characterized by 12 stations for data collection separated by long walks. Data collected on astronaut walking speed provide operational times included in traverse models calculated for this ROI. Traverse coordinates and way points summaries for both Apollo EVAs can be found in the supplementary material (SP-A). The Apollo 12 EVA 2 traverse lasted approximately 2 h and 45 min, of which only ~30 min were spent walking [56]. The astronauts covered almost 1.6 km, reaching a distance of ~400 m from the lander, including a 100 m segment at 14◦ inclination. The EVA recovered ~18 kg of geological samples, including cores (~60 cm deep), and rocks from trenched (~20 cm) material [71]. For this EVA, we calculated an average speed of 0.56 ± 0.39 ms− 1 or 2.02 ± 1.40 kmh− 1 (mean±1σ, No = 25), and a median speed of 0.42 ms− 1 or 1.51 kmh− 1. The Apollo 14 EVA 2 traverse lasted ~4.5 h, during which time the astronauts covered ~2.9 km, reaching a distance ~1.4 km from the lander. Approximately 22 kg of geological samples were recovered, Fig. 7. Top: Apollo 12 EVA 2, with tie points (block dots) created by linking including core (~60 cm deep) and trenched (~30 cm) material [71]. times acknowledged in official transcripts with geological observations and Due to challenges walking over the rugged terrain, the crew fell behind procedures completed on the surface. Bottom: Repeated for Apollo 14 EVA 2. schedule; notably, the MET proved difficult to transport and for portions of the EVA the crew resorted to carrying rather than pulling it [56]. A information). We searched for the largest pixel step before significant summary table of this EVA from Biomedical Results of Apollo [55] in­ traverse features are overlooked, which produces notable variations in cludes traverse speed between stations, averaging 0.81 ± 0.38 ms− 1 or the distance with small changes. We estimated this sampling interval for 2.92 ± 1.37 kmh− 1 (mean±1σ, No = 13). Because a linear distance is smoothing to generate the minimum realistic distance by increasing the used, this is an underestimate. We calculate a mean speed of 0.84 ± pixel size step until a non-stationary state is reached. An augmented 0.48 ms− 1 or 3.02 ± 1.73 kmh− 1 (mean±1σ, No = 35) and a median of Dickey-Fuller test [69] allows the stationary trend of the path to be 0.62 ms− 1 or 2.23 kmh− 1. analyzed with a confidence level of 99 %, evaluating the deviation of a Plotting speed against slope (in the direction of the traverse) in­ polynomial fit with at least R2 = 0.8 (Fig. 4 right). A straight-line tra­ dicates a weak positive correlation of noisy data points (y = verse will always result in the same computed distance regardless of the − 0.01x+0.75; R2 = 0.03; units in ms− 1), potentially suggesting pixel size, whilst a meandering path will vary drastically at some decreasing speed with a higher slope. Because Apollo 14 involved the pixel-smoothing steps based on the curve shapes. cumbersome MET, this trend represents traverse speed with a MET alternated between two astronauts, where the position of only one of the 4. Data products and results pair was tracked. We take forward an average of the three calculations, returning a mean speed of 0.74 ms− 1 or 2.66 kmh− 1. 4.1. Base maps 4.3. Mapped PSRs and boulders Fig. 5 displays the base maps derived from LOLA data elaborated in Section 3: 5 m/pixel elevation with 20 m contours, 5 m/pixel slope 521 PSRs were mapped within the ~300 km2 ROI encompassing the derived from LDEM, NAC mosaic, and bearing capacity generated using rim of Shackleton crater and the Shackleton-Henson ridge, incorpo­ LDSM. Bearing capacity varies from ~0 to 13.2 kN/m2, in agreement rating those analyzed by Ref. [72] derived from the 60 m product by with maps generated for the Shackleton-Hansen ridge region encom­ Ref. [2]. The mean PSR area is 11,975 m2, with a significantly skewed passing potential landing sites 001 and 004 [5]. distribution (median = 1075 m2, standard deviation = 100,859 m2) From 240 m/pixel summer Diviner data (defined as where the sub­ towards smaller sizes. PSRs range from 75 m2 to 2,144,700 m2, or be­ solar latitude is in the Southern hemisphere at noon local time), we tween ~10 m and ~1600 m in diameter. The PSRs within the ROI have generated average, minimum, and maximum temperature maps, as well an average LDEC coverage of 11.22 ± 2.68 % (mean±1σ, No = 521), as local time maps to evaluate both the lowest PSR temperature and with a median of 10.8 %. Geolocation uncertainty for the 5 m/pixel DEM highest temperature encountered during a traverse. Over a 6-h EVA, for is ~10–20 cm horizontally and ~2–4 cm vertically for each pixel [17, 331 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 8. Combined traverse metrics from Apollo 12 EVA 2 (blue) and Apollo 14 EVA 2 (red and yellow) derived from Lunar Surface Journal transcripts and Biomedical Results of Apollo (1975) [70]. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.) Fig. 9. Left: Distribution of PSRs within the ROI, overlaid on NAC 1 m/pixel imagery. Circles denote craters with potential to host areas of permanent shadow. Right: PSR edge distribution within the ROI, overlaid on a slope map generated from 5 m/pixel LDEM with elevation contour lines. Diamonds represent boulders. The 2 km radius perimeter is depicted. Data credits: NASA/LROC/GSFC/ASU. Table 1 Table 2 Table showing the number of traverses to PSRs with Table showing the number of traverses to PSRs within 2 km radially of potential slopes below 5, 10, and 15◦ . landing sites 001 and 004 and location 001(6) with slopes below 10◦ and 15◦ . PSRs accessible ROI 001 001(6) 004 <15◦ slope 490 (94 %) # of PSRs 22 20 10 <10◦ slope 351 (67 %) <15◦ slope 20 19 10 <5◦ slope 74 (14 %) <10◦ slope 4 4 0 332 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 10. Traverse paths within 2 km radius of potential landing site 001 to crater edges that host PSRs. Location 001(6) is labeled for reference. Indexed PSRs from Ref. [72]. 46]. 4.4. Traverse and descent to PSRs Fig. 9 provides a visual representation of the distribution of PSRs within the ROI in this study. This figure includes the overlay of boulders An accessible traverse was defined as a walking EVA where the that were extracted from Ref. [8]. The inclusion of boulder locations maximum slope does not exceed 15◦ . Under this definition, 94 % of the offers insights into the spatial relationship between PSRs and these PSRs are accessible from their respective host crater rim. We also geological features, thereby imposing constraints on possible traverses considered more amiable conditions and determined that with a and exploration targets. We capture many smaller PSRs using the finer 5 maximum slope of 10◦ and 5◦ , nearly 67 % and 14 % of PSRs are m/pixel resolution, resulting in high densities of possible targets around accessible, respectively (Table 1). both potential landing sites 001 and 004. The highest overall densities of There are collectively 34 PSRs within a 2 km radial distance of the PSRs are found on the flanks of Shackleton crater on either side of the two potential landing sites 001 (including flat landing location 001(6)) Shackleton-Henson ridge. When comparing the generated PSRs to a and 004 (Table 2). Note that because there is only a ~400 m distance slope map, we find PSR density is much lower on steep slopes. This is between 001 and 001(6), 18 PSRs are accessible from both (see Fig. 10). likely due to a combination of a more generous illumination and a lower Fig. 11 depicts the percentage of a traverse path below 5◦ . Location 001 density of craters, which erode quicker on steeper slopes [73]. (6) has the largest number of traverses where 75 % or more of the tra­ verse is on slopes <5◦ . The metabolic demand on astronauts is thus 333 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 best convey the topography. The atlas includes the 521 PSRs identified within the ROI, accom­ panied by host crater and PSR properties, such as shadowed area for 2◦ and 5◦ Sun elevation, temperature, coverage (percentage of data points not interpolated), and radius and depth of the host crater (calculated by fitting a plane to the rim for slope correction, prior to computing maximum elevation change). Each PSR spread consists of (1) the optimal descent from any point on 1.1 x crater rim radius to PSR edge, and continued to its center, for all identified in the ROI (SP–B), and (2) the minimum-cost path from a potential landing site to the PSR edge, continued to its center, if accessible within 2 km radially of 001, 004, or 001(6) (SP–C). An example from the atlas can be found in the Appendix: Figure A1 illustrates a traverse from potential landing site 001, Figure A2 exem­ plifies the spread with associated general values, and Figure A3 offers an optimal crater descent to PSR center. 5. Discussion Fig. 11. Percentage of route with slopes less than 5◦ for traverses within 2 km 5.1. Pathfinding of potential landing sites 001 and 004 and location 001(6). A quick overview of 521 potential crater descents across variable surface terrain is enabled with the automated computation process to inform EVA opportunities and route-planning. The number of round-trip traverses achievable, notably under 30 min, is promising for the possible diversity of sample conditions. Astronauts need to conserve energy and manage metabolic heat to ensure that they can return to their starting point safely, with sufficient surplus for geological sample collection, which may involve strenuous activities such as hammering, trenching, and coring. EVA execution will undoubtedly also be shaped by the as­ tronauts performing them. Activities along the suggested routes will be influenced by spacesuit thermal measurements [76], to plan future EVA circuits more comprehensively in response to human metabolic predictions. Additionally, we manually checked and modified two of the auto­ mated traverses for testing and comparison purposes. Although we used the highest LDEM resolution currently available (5 m/pixel LOLA DEM; [46]), its resolution is still too coarse to account for all surface variations discernible to astronauts. For manual traverse mapping, a NAC mosaic with a resolution of 1 m/pixel was used. This allows users to identify and avoid small craters larger than ~2–3 m diameter, as well as other Fig. 12. Number of (round-trip) traverses that can be walked within different potentially hazardous features. Deviation from the automated traverse time ranges. should be considered when (i) smoothing in areas of gentle slope, (ii) avoiding small potentially hazardous features, and (iii) obtaining spec­ expected to be lower. EVA planners using these traverses could incor­ imens for scientific interest or resource development. Automatic tra­ porate longer walking distances between breaks or include more stren­ verses can even increase the distance walked to reduce the cumulative uous tasks such as trenching and coring without risking exhaustion. slope by making switchbacks. The automated traverse is constrained to Fig. 12 highlights the time it takes to make a return trip to PSRs from the the 5 m/pixel raster grid and thus creates a step-like pattern that may potential landing sites, using the average Apollo-derived speed (Section not be realistic for an astronaut walking on the Moon. Manual traverse 4). All traverses can be completed in less than 2 h, assuming a constant planning can smooth this feature in areas where possible. However, it walking speed of 0.74 ms− 1 (or 2.66 kms− 1), with no stops along the does not guarantee that the drawn route is closer to natural astronaut way. Traverses from 004 all take less than 1.5 h but feature a higher movements due to the absence of a 3D perspective. average slope. There are a total of six round-trip traverses into PSRs from When comparing automated and manual traverses, there is a negli­ sites 001, 001(6), and 004 that can be completed in under 30 min. These gible elevation change among traverses and users. Distance traveled will give ample time for diversions and other activities. between automatic and manual traverses differs slightly. In most cases, the manual traverse distance is usually lower than the automated tra­ verse (before applying the minimum realistic distance smoothing), 4.5. Atlas which can be explained by the smoothness of the user-defined path versus the jaggedness of the automated one. The average slope is always All traverses from potential landing sites, along with the optimal lower for the automated traverse. As a minimum-cost path algorithm crater descent, have been compiled in an atlas found in the Supple­ that uses slope as its main input, this result is expected. Any deviation mentary Material. Distance, elevation change, slope, bearing capacity, from the automated path would increase the average slope. When temperature, illumination, direct view from the HLS, and duration comparing the maximum slope between the traverse approaches no (including the return, ‘bck’) are evaluated for each traverse. Atlas im­ trends are discerned. The comparison shows that in some instances the ages were generated with Python using the Mayavi package [74] and maximum slope can be reduced to the detriment of the total cumulative Matplotlib [75]. For 3D renderings the scene illumination was selected to slope. Fig. 13 presents a comparison between the path generated by the 334 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 13. Comparison of traverses to PSRs between two user-drawn paths and path-finder algorithm result. Left panel shows the traverses overlaid on the slope map. Right panels show the traverses overlaid on NAC images. path-finder algorithm developed in this study and two alternative paths the importance of these factors and their prospective integration into created by users. The users manually smoothed the paths and introduced future software iterations. detours based on visual inspection of NAC images. While the automated Both the MoonPath tool and manual mappers need to download traverse may be slightly longer, the significant reduction in metabolic suitable orbital data, demanding a comparable time investment. Once workload achieved through lower cumulative slopes ensures optimal the data is downloaded, our pipeline produces results within seconds or energy management during EVAs. minutes, whereas manual mapping may extend to hours or days. This exhaustive path-finding approach can be applied both to eval­ Crucially, this expedited automated method enables mission planners to uate the range of accessible targets around potential landing sites and explore a broader array of quantitatively optimized options. assist candidate site rankings, as well as a first EVA filter around those eventually selected. We recommend that manual traverse planning should subsequently be done with high-resolution lunar surface images 5.2. Traverse properties after down-selecting from the automated traverses to avoid potentially hazardous features unaccounted for. Only one of the accessible PSRs has a maximum temperature below Astronaut EVA design involves a multi-faceted approach, factoring in 107 K (surface water ice persistence threshold [77], suggesting highest several variables affecting metabolic workload. While our study em­ potential for appreciable volumes of frozen volatiles). This PSR phasizes distance and elevation changes for efficient round-trip traverse (SP_895711_1611230) should be reviewed as a potential target. How­ planning, we recognize the significance of additional parameters, such ever, it is outside the 2 km range of potential landing sites 001, 001(6), as temperature fluctuations and bearing capacity. Sunlight incidence and 004 imposed in this study. impacts operations and equipment performance, whilst terrain charac­ For each traverse, the Sun position can vastly change experienced teristics are essential for safe mobility. Integrating these variables could illumination conditions. As an example of the dramatically different enhance traverse optimization. Illumination, communication con­ outcomes, we observe that the most and least illuminated traverses are straints, and mission goals are also relevant considerations. Sun position inverted over a period of two weeks. Since potential landing site 001 is and local topography affect visibility and power generation, while on the crest of the Shackleton-Henson ridge, depending on which flank a communication constraints impact real-time support. We acknowledge traverse passes over, the path could be wholly illuminated or completely in shadow. 335 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. 14. Computed traverses from site 001 to PSR (closed thick white lines) SP_894764_1367750, SP_894748_1380060, and SP_894813_1378000, overlaid on a slope map with elevation contour lines. The slope profiles of each traverse are shown as a function of the distance traveled by the astronaut. They are categorized into three groups: computed using the 5 m/pixel resolution, 1 m/pixel resolution, and 5 m/pixel resolution interpolated to the 1 m/pixel resolution. A bar chart is also presented to illustrate the distribution of traverses based on pixels they transect, classified into those with slopes above and below 5◦ . The horizontal dashed line denotes the slope threshold of 15◦ . Thin white lines superimposed on each map depict the traverses from the alternative resolution to enable easy visual comparison. Temporal considerations are needed given that conditions such as 5.3. DEM resolution dependency temperature and illumination can vary significantly. For traverses using illumination conditions on 16 and December 30, 2025, four traverses To assess the impact of DEM resolution on the traverses, we from 004 and one from 001(6) are more than half conducted in shadow. employed a 1 m/pixel DEM generated from NAC images using the shape- Specific illumination will vary for other dates, so traverses will need to from-shading algorithm [80,81]. This high-resolution DEM covers a 1 be considered not only for their scientific targets but the surface km × 1 km area at site 001, where three mapped PSRs are located. By environment. utilizing this detailed topographic data, we computed the slope map and Regarding astronaut walking speed, the walk-to-run transition of applied our methodology to determine the minimum-cost path. 1.42 ± 0.24 ms− 1 (5.11 ± 0.86 kmh− 1) calculated by Ref. [78] was used In Fig. 14, we present the three computed traverses from site 001 to as a reference for comparison. This value matches the upper limit for the PSRs, superimposed on a slope map with elevation contour lines. speed calculated between most way points, suggesting that for sections Additionally, we illustrate the slope profiles of each traverse as a func­ of the traverse, Apollo astronauts were walking as fast as they could in tion of the distance traveled by the astronaut. For illustration purposes, lunar gravity. In case the rover broke down during Apollo 17 and as­ the distance measurements are not adjusted using the same correction tronauts had to walk to the LEM, NASA used estimated speeds of 1 ms− 1 method as previously described, so distance may be overestimated, (3.6 kmh− 1), or 0.75 ms− 1 (2.7 kmh− 1) if the remaining traverse was particularly for the 1 m/pixel map. over an hour [79]. These figures are consistent with those plotted in Some differences are evident in the calculated traverses, with vari­ Fig. 8. During Artemis III, a nominal speed of 2 kmh− 1 is expected on ations observed in the approach to crater rims and the descent towards level surfaces, although this would drop significantly over more chal­ the edges of the PSRs. Utilizing a higher resolution slope map results in lenging terrain [65]. Recent simulations of lunar EVAs using the NASA meandering paths with less time spent in straight lines, leading, as ex­ Mark III suit walked at a comparable speed of 0.74 ms− 1 (2.7 kmh− 1) pected, to longer routes. However, the red path in the 5 m/pixel traverse and 0.83 ms− 1 (3.0 kmh− 1) over a minimum of 500 m with slopes − 10 % covers a greater distance as it approaches the PSR from the north. to +30 % [76]. Increased spacesuit mobility is likely to allow astronauts Conversely, the higher resolution path finds a more efficient descent to move and collect data faster, as well as work more independently. with less overall walking, maintaining slopes below the specified threshold. Despite the orange path covering an additional ~250 m, it 336 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 achieves a maximum slope of ~8◦ , compared to ~10◦ in the lower Dijkstra’s minimum cost path algorithm to compute the optimal route resolution traverse. The updated map also reveals a steeper slope within for EVAs with the most efficient workload criterion, i.e., the traverse to the host crater, prompting the algorithm to avoid it. The magenta tra­ PSRs with the minimum cumulative slope. We have also evaluated verse is slightly longer, with a distinct descent pattern towards the PSR, temperature, bearing capacity, astronaut illumination, and the albeit exhibiting similar slope profiles. astronaut-to-lander direct view along the traveled distance. Based on To facilitate a comprehensive comparison, we interpolated the tra­ estimated average path times from Apollo 12 and 14 transcripts, we verses obtained using the 5 m/pixel map. Their superposition on the 1 identify traverses from potential landing sites 001, 001(6), and 004 to m/pixel map reveals a notable degradation in the slope profile, sur­ PSRs accessible within a 2 km radius under 2 h round-trip. We find that passing the threshold for two of the traverses. Fig. 14 analysis demon­ 94 % of all PSRs in the area are accessible from the rim on slopes below strates that despite a slight increase in the distance covered, the 15◦ . Twenty and 19 PSRs are accessible from potential landing sites 001 optimized paths consistently exhibit lower cumulative slope. This is and 001(6) respectively, four of which are accessible on slopes entirely evident in the bar chart as there is a reduction of the number of pixels below 10◦ . Traverses around site 004 are more workload-demanding. with slopes exceeding 5◦ . To facilitate future mission planning, we compiled an atlas (attached The running time bounds of a minimum-cost pathfinder can be in the Supplementary Material) that includes all 521 traverses and de­ defined as a function of the number of edges (m) and the number of scents to PSRs. This type of information is critical for determining the vertices (n). Considering the implementation of binary heaps for priority most efficient circuits to optimize astronaut EVAs and identify accessible queues, the theoretical efficiency of Dijkstra’s algorithm for connected potential science targets. Overall, the developed pipeline and traverse graphs is proportional to m⋅log(n) [82]. The running time for the three atlas can be used to support mission planning for sample collection of traverses compared in this section increases approximately 24 times potential near-surface ice in the PSRs of the lunar south polar region to when incrementing the cost map resolution by a factor of 5. On average, address major scientific priorities. the computation of each traverse compiled in the atlas and its associated While the utility of the MoonPath tool was demonstrated to reach properties from site 001 to PSR took 74 ± 28 s on a 2.3 GHz Intel Core i9 PSRs, the pipeline can be used to calculate minimum workload astronaut (I9–9980HK) processor. paths to any other geologic and exploration targets within the AEZ or Our analysis highlights the importance of using meter or sub-meter elsewhere on the Moon. DEM resolutions for calculating optimal traverses for walking EVAs. The findings suggest that automated paths with lower resolution maps may deviate from the slopes experienced at the scale of an astronaut’s Declaration of competing interest footstep. By utilizing higher resolution DEMs, we can achieve more accurate and representative slope calculations. The authors declare that they have no known competing financial Unfortunately, during the course of this study, sub-meter DEM maps interests or personal relationships that could have appeared to influence were not available. Nevertheless, once such maps are generated, they the work reported in this paper. can be readily incorporated into our software tool. This flexibility pre­ sents a promising avenue for future research and implementation, as the Acknowledgments utilization of sub-meter DEMs would enhance the accuracy of automated calculations for determining optimal traverses. E. P. A. thanks funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation 6. Conclusions programme (grant agreement No. 865657). J. S. is supported by funding from the European Union’s Horizon 2020 research and innovation The Artemis program seeks to return humans to the lunar surface and programme under the Marie Skłodowska-Curie grant agreement No. specifically the south polar region, where PSRs may host near-surface 847439. We thank the LRO team for their efforts to acquire the data used ice, making them critical targets for sample collection and scientific in this study, as well as the staff at the Lunar and Planetary Institute for analysis. To design astronaut EVAs, we developed a Python pipeline that their support during an Exploration Science internship through the automatically models and evaluates the optimized path to all accessible Center for Lunar Science and Exploration, where this research was PSRs given a starting point within the vicinity of the ‘Connecting Ridge’ conducted. We are also grateful to Bo Wu for generating the 1 m/pixel region. Using high-resolution LOLA data, we identified and mapped 521 DEM and Sarah Boazman for sharing the boulder locations. This work PSRs that maintain a minimum area of 75 m2 nearby potential landing was supported by NASA Solar System Exploration Research Virtual sites 001 and 004, and a flat landing zone 001(6). Institute (80NSSC20M0016, PI D.A.K.). LPI Contribution No. 3009. LPI Our MoonPath pipeline combines a Monte Carlo approach with is operated by the Universities Space Research Association. 337 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Appendix A Fig. A1. Example spread of the traverse and descent, as well as a 2D plot with elevation contours, a 3D plot using 2 m/pixel NAC images and 5 m/pixel LOLA DEM, and a histogram of the distance traveled as a function of the slope. 338 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. A2. Example of the tables associated with each traverse with general values calculated, and the 2 m/pixel NAC image and a detailed 2D map of the host crater. 339 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 Fig. A3. Example of the tables associated with each PSR optimal descent with general values calculated, and a detailed 2D and 3D image of the host crater. Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.actaastro.2023.10.010. References [7] N.R. Council, The Scientific Context for Exploration of the Moon, The National Academies Press, Washington, DC, 2007, https://doi.org/10.17226/11954. [8] S.J. Boazman, J. Shah, Harish, A.J. Gawronska, S.H. Halim, A.V. Satyakumar, C. [1] D.B.J. Bussey, J.A. McGovern, P.D. Spudis, C.D. Neish, H. Noda, Y. Ishihara, S. M. Gilmour, V.T. Bickel, N. Barrett, D.A. Kring, The distribution and accessibility of A. Sørensen, Illumination conditions of the south pole of the Moon derived using geologic targets near the lunar south Pole and candidate Artemis landing sites, Kaguya topography, Icarus 208 (2010) 558–564, https://doi.org/10.1016/j. Planet. Sci. J. 3 (2022) 275, https://doi.org/10.3847/PSJ/ACA590. icarus.2010.03.028. [9] H. Bernhardt, M.S. Robinson, A.K. Boyd, Geomorphic map and science target [2] E. Mazarico, G.A. Neumann, D.E. Smith, M.T. Zuber, M.H. Torrence, Illumination identification on the Shackleton-de Gerlache ridge, Icarus 379 (2022), 114963, conditions of the lunar polar regions using LOLA topography, Icarus 211 (2011) https://doi.org/10.1016/J.ICARUS.2022.114963. 1066–1081, https://doi.org/10.1016/j.icarus.2010.10.030. [10] S.H. Halim, N. Barrett, S.J. Boazman, A.J. Gawronska, C.M. Gilmour, Harish, [3] E.J. Speyerer, S.J. Lawrence, J.D. Stopar, P. Gläser, M.S. Robinson, B.L. Jolliff, K. McCanaan, A.V. Satyakumar, J. Shah, D.A. Kring, Numerical modeling of the Optimized traverse planning for future polar prospectors based on lunar formation of Shackleton crater at the lunar south pole, Icarus 354 (2021), https:// topography, Icarus 273 (2016) 337–345, https://doi.org/10.1016/j. doi.org/10.1016/j.icarus.2020.113992. icarus.2016.03.011. [11] A.J. Gawronska, N. Barrett, S.J. Boazman, C.M. Gilmour, S.H. Halim, Harish, [4] NASA, The Artemis III Science Definition Team Report, 2020. https://www.nasa. K. McCanaan, A.V. Satyakumar, J. Shah, H.M. Meyer, D.A. Kring, Geologic context gov/sites/default/files/atoms/files/artemis-iii-science-definition-report-1204 and potential EVA targets at the lunar south pole, Adv. Sp. Res. 66 (2020) 2020c.pdf. (Accessed 26 July 2022). 1247–1264, https://doi.org/10.1016/j.asr.2020.05.035. [5] D.A. Kring, V.T. Bickel, A.L. Fagan, L. Gaddis, H. Hiesinger, J.M. Hurtado, [12] D.A. Kring, Lunar South Pole geology: preparing for a seventh lunar landing, in: T. Huning, L. M, C.A. Looper, G.R. Osinski, S.M. Tikoo, C.H. van der Bogert, NASA Explor. Sci. Forum 2019, 2019. Assessing landing and EVA options in the vicinity of potential Artemis landing site [13] P.J. Adams, E. Stuart-Alexander, Geologic map of the central far side of the Moon, 001, in: NASA Explor, Sci. Forum, Boulder, 2022. https://dl.airtable.com/.attach Sheet I-1047. 1:5 000 000 (1978), https://doi.org/10.2307/634119. ments/83b4edad0f398cd4489452d64ebdab18/e50f092b/KringEtAl_NESF2022 [14] I. Garrick-Bethell, K. Miljković, H. Hiesinger, C.H. van der Bogert, M. Laneuville, D. _Site001LandingAndEVAOptions_final.pdf?ts=1658976045&userId=usr L. Shuster, D.G. Korycansky, Troctolite 76535: a sample of the Moon’s South Pole- lVLEMF3U1302KF&cs=2172c1f4355b4c0a. Aitken basin? Icarus 338 (2020), 113430 https://doi.org/10.1016/J. [6] K. Watson, B.C. Murray, H. Brown, The behavior of volatiles on the lunar surface, ICARUS.2019.113430. J. Geophys. Res. 66 (1961) 3033–3045, https://doi.org/10.1029/ jz066i009p03033. 340 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 [15] H. Hiesinger, C.H. Van Der Bogert, J.H. Pasckert, L. Funcke, L. Giacomini, L. g8Ttwfuoh8aXohb_KYblyX0l_rPrU5y2uGQtU-udzhocaPJUD3iHZ4Ri9Oxw-43DkQ. R. Ostrach, M.S. Robinson, How old are young lunar craters? J. Geophys. Res. (Accessed 3 March 2023). Planets. 117 (2012) https://doi.org/10.1029/2011JE003935, 0–10. [42] NASA, Human Landing System Concept of Operations, 2019. [16] A. Morbidelli, S. Marchi, W.F. Bottke, D.A. Kring, A sawtooth-like timeline for the [43] C. Cunningham, J. Amato, H.L. Jones, W.L. Whittaker, Accelerating energy-aware first billion years of lunar bombardment, Earth Planet Sci. Lett. 355 (356) (2012) spatiotemporal path planning for the lunar poles, in: Proc. - IEEE Int. Conf. Robot. 144–151, https://doi.org/10.1016/j.epsl.2012.07.037. Autom., 2017, pp. 4399–4406, https://doi.org/10.1109/ICRA.2017.7989508. [17] P. Gläser, F. Scholten, D. De Rosa, R. Marco Figuera, J. Oberst, E. Mazarico, G. [44] P.A. Plonski, P. Tokekar, V. Isler, Energy-efficient path planning for solar-powered A. Neumann, M.S. Robinson, Illumination conditions at the lunar south pole using mobile robots, J. F. Robot. 30 (2013) 583–601, https://doi.org/10.1002/ high resolution digital terrain models from lola, Icarus 243 (2014) 78–90, https:// rob.21459. doi.org/10.1016/j.icarus.2014.08.013. [45] J. Schlutz, E. Messerschmid, Integrating advanced mobility into lunar surface [18] R.W.K. Potter, G.S. Collins, W.S. Kiefer, P.J. McGovern, D.A. Kring, Constraining exploration, Acta Astronaut. (2012) 15–24, https://doi.org/10.1016/j. the size of the South Pole-Aitken basin impact, Icarus 220 (2012) 730–743, https:// actaastro.2012.01.005. doi.org/10.1016/j.icarus.2012.05.032. [46] M.K. Barker, E. Mazarico, G.A. Neumann, D.E. Smith, M.T. Zuber, J.W. Head, [19] D.J. Lawrence, A tale of two poles: toward understanding the presence, Improved LOLA elevation maps for south pole landing sites: error estimates and distribution, and origin of volatiles at the polar regions of the Moon and Mercury, their impact on illumination conditions, Planet. Space Sci. 203 (2021), https://doi. J. Geophys. Res. Planets. 122 (2017) 21–52, https://doi.org/10.1002/ org/10.1016/j.pss.2020.105119. 2016JE005167. [47] B. Day, E. Law, NASA’S Moon Trek: extending capabilities for lunar mapping and [20] M. Lemelin, P.G. Lucey, A. Camon, Compositional maps of the lunar polar regions modeling, in: COSPAR Sci. Assem, 2018, pp. 11–18. B3.1. derived from the kaguya spectral profiler and the lunar orbiter laser altimeter data, [48] M.S. Robinson, S.M. Brylow, M. Tschimmel, D. Humm, S.J. Lawrence, P.C. Thomas, Planet. Sci. J. 3 (2022) 63, https://doi.org/10.3847/psj/ac532c. B.W. Denevi, E. Bowman-Cisneros, J. Zerr, M.A. Ravine, M.A. Caplinger, F. [21] A.N. Deutsch, J.W. Head, G.A. Neumann, Analyzing the ages of south polar craters T. Ghaemi, J.A. Schaffner, M.C. Malin, P. Mahanti, A. Bartels, J. Anderson, T. on the Moon: implications for the sources and evolution of surface water ice, Icarus N. Tran, E.M. Eliason, A.S. McEwen, E. Turtle, B.L. Jolliff, H. Hiesinger, Lunar 336 (2020), https://doi.org/10.1016/j.icarus.2019.113455. reconnaissance orbiter camera (LROC) instrument overview, Space Sci. Rev. 150 [22] A.R. Tye, C.I. Fassett, J.W. Head, E. Mazarico, A.T. Basilevsky, G.A. Neumann, D. (2010) 81–124, https://doi.org/10.1007/s11214-010-9634-2. E. Smith, M.T. Zuber, The age of lunar south circumpolar craters Haworth, [49] R.V. Wagner, E.J. Speyerer, M.S. Robinson, LROC team, new mosaicked data Shoemaker, Faustini, and Shackleton: implications for regional geology, surface products from the LROC team, 46th Lunar Planet, Sci. Conf. 46 (2015) 1473. processes, and volatile sequestration, Icarus 255 (2015) 70–77, https://doi.org/ [50] ESRI, ENVI EX user’s guide, Esri (2009) 275. 10.1016/j.icarus.2015.03.016. [51] D.A. Paige, M.C. Foote, B.T. Greenhagen, J.T. Schofield, S. Calcutt, A.R. Vasavada, [23] D.A. Kring, G.Y. Kramer, D.B.J. Bussey, D.M. Hurley, A.M. Stickle, C.H. van der D.J. Preston, F.W. Taylor, C.C. Allen, K.J. Snook, B.M. Jakosky, B.C. Murray, L. Bogert, Prominent volcanic source of volatiles in the south polar region of the A. Soderblom, B. Jau, S. Loring, J. Bulharowski, N.E. Bowles, I.R. Thomas, M. Moon, Adv. Sp. Res. 68 (2021) 4691–4701, https://doi.org/10.1016/J. T. Sullivan, C. Avis, E.M. De Jong, W. Hartford, D.J. McCleese, The lunar ASR.2021.09.008. reconnaissance orbiter diviner lunar radiometer experiment, Space Sci. Rev. 150 [24] K. Donaldson Hanna, M. Wyatt, C. Pieters, L. Cheek, P. Isaacson, D. Paige, (2010) 125–160, https://doi.org/10.1007/s11214-009-9529-2. B. Greenhagen, Diviner and Moon mineralogy mapper integrated observations of [52] J.P. Williams, B.T. Greenhagen, D.A. Paige, N. Schorghofer, E. Sefton-Nash, P. plagioclase-rich regions on the Moon, in: Annu. Lunar Planet. Sci. Conf., 42nd, O. Hayne, P.G. Lucey, M.A. Siegler, K.M. Aye, Seasonal polar temperatures on the 2011. Moon, J. Geophys. Res. Planets. 124 (2019) 2505–2521, https://doi.org/10.1029/ [25] P.B. James, D.E. Smith, P.K. Byrne, J.D. Kendall, H.J. Melosh, M.T. Zuber, Deep 2019JE006028. structure of the lunar south Pole-aitken basin, Geophys. Res. Lett. 46 (2019) [53] V.T. Bickel, D.A. Kring, Lunar south pole boulders and boulder tracks: implications 5100–5106, https://doi.org/10.1029/2019GL082252. for crew and rover traverses, Icarus 348 (2020), 113850, https://doi.org/10.1016/ [26] P.D. Spudis, B. Bussey, J. Plescia, J.-L. Josset, S. Beauvivre, Geology of Shackleton J.ICARUS.2020.113850. crater and the south pole of the Moon, Geophys. Res. Lett. 35 (2008), L14201, [54] W.D. Carrier III, G.R. Olhoeft, W. Mendell, Physical properties of the lunar surface, https://doi.org/10.1029/2008GL034468. in: Lunar Sourceb., 1991, pp. 522–530. [27] M. Hirabayashi, B.A. Howl, C.I. Fassett, J.M. Soderblom, D.A. Minton, H.J. Melosh, [55] J.M. Waligora, D.J. Horrigan, Metabolism and heat dissipation during Apollo EVA The role of breccia lenses in regolith generation from the formation of small, simple periods, in: Biomed. Results Apollo, 1975, pp. 115–128. NASA SP-368), https craters: application to the Apollo 15 landing site, J. Geophys. Res. Planets. 123 ://books.google.co.in/books?hl=en&lr=&id=oyFsAAAAMAAJ&oi=fnd&pg=PA (2018) 527–543, https://doi.org/10.1002/2017JE005377. 115&dq=Metabolism+and+heat+dissipation+during+Apollo+EVA+periods&ots [28] J.W. Head, L. Wilson, Generation, ascent and eruption of magma on the Moon: new =XxTnab_4yo&sig=br8TEM4kVU0LoHc5IYSu0uJpszk. (Accessed 27 March 2023). insights into source depths, magma supply, intrusions and effusive/explosive [56] M. Jones, K. Glover, Apollo Lunar Surface Journal, NASA Website, 2013. eruptions (Part 2: predicted emplacement processes and observations), Icarus 283 https://www.hq.nasa.gov/alsj/main.html. (Accessed 2 August 2022). (2017) 176–223, https://doi.org/10.1016/j.icarus.2016.05.031. [57] H. Noda, H. Araki, S. Goossens, Y. Ishihara, K. Matsumoto, S. Tazawa, N. Kawano, [29] H. Lv, Q. He, X. Chen, P. Han, Numerical simulation of impact crater formation and S. Sasaki, Illumination conditions at the lunar polar regions by KAGUYA(SELENE) distribution of high-pressure polymorphs, Acta Astronaut. 203 (2023) 169–186, laser altimeter, Geophys. Res. Lett. 35 (2008), https://doi.org/10.1029/ https://doi.org/10.1016/j.actaastro.2022.11.048. 2008GL035692. [30] K.M. Cannon, A.N. Deutsch, J.W. Head, D.T. Britt, Stratigraphy of ice and ejecta [58] NASA JPL Solar System Dynamics Group, Horizons System, JPL Website, 2017. deposits at the lunar Poles, Geophys. Res. Lett. 47 (2020), https://doi.org/ https://ssd.jpl.nasa.gov/horizons/app.html#/. (Accessed 2 August 2022). 10.1029/2020GL088920. [59] S. Bryant, Lunar pole illumination and communications statistics computed from [31] C.J.T. Udovicic, K.R. Frizzell, G.R.L. Kodikara, M. Kopp, K.M. Luchsinger, GSSR elevation data, in: SpaceOps 2010 Conf, 2010, https://doi.org/10.2514/ A. Madera, M.L. Meier, T.G. Paladino, R.V. Patterson, F.B. Wroblewski, D.A. Kring, 6.2010-1913. Buried ice deposits in lunar polar cold traps were disrupted by ballistic [60] M.A. Siegler, B.G. Bills, D.A. Paige, Effects of orbital evolution on lunar ice sedimentation, J. Geophys. Res. Planets (2023), e2022JE007567, https://doi.org/ stability, J. Geophys. Res. Planets. 116 (2011), https://doi.org/10.1029/ 10.1029/2022JE007567. 2010JE003652. [32] C.E. Carr, D.J. Newman, K.V. Hodges, Geologic traverse planning for planetary [61] E.M.A. Chen, F. Nimmo, Tidal dissipation in the lunar magma ocean and its effect EVA, SAE Tech. Pap. (2003), https://doi.org/10.4271/2003-01-2416. on the early evolution of the Earth-Moon system, Icarus 275 (2016) 132–142, [33] P.S. Dodds, D.H. Rothman, Scaling, universality, and geomorphology, Annu. Rev. https://doi.org/10.1016/j.icarus.2016.04.012. Earth Planet Sci. 28 (2000) 571–610, https://doi.org/10.1146/annurev. [62] W.R. Ward, Past orientation of the Lunar spin axis, Science 189 (1975) 377–379, earth.28.1.571. https://doi.org/10.1126/science.189.4200.377. [34] E.W. Dijkstra, A note on two problems in connexion with graphs, Numer. Math. 1 [63] J.J. Marquez, Human-Automation Collaboration: Decision Support for Lunar and (1959) 269–271, https://doi.org/10.1007/BF01386390. Planetary Exploration, 2007. [35] L.E. Kavraki, P. Švestka, J.C. Latombe, M.H. Overmars, Probabilistic roadmaps for [64] J. Norheim, J. Hoffman, D. Newman, T.E. Cohen, D.S. Lees, M.C. Deans, D.S.S. Lim, path planning in high-dimensional configuration spaces, IEEE Trans. Robot. Architecture of a surface exploration traverse analysis and navigational tool, IEEE Autom. 12 (1996) 566–580, https://doi.org/10.1109/70.508439. Aerosp. Conf. Proc. (2018) 1–11, https://doi.org/10.1109/AERO.2018.8396510, [36] S. LaValle, Rapidly-exploring Random Trees: A New Tool for Path Planning, 1998. 2018-March. [37] S. Karaman, M.R. Walter, A. Perez, E. Frazzoli, S. Teller, Anytime motion planning [65] NASA, Exploration EVA System Concept of Operations, 2020. https://ntrs.nasa. using the RRT, Proc. - IEEE Int. Conf. Robot. Autom. (2011) 1478–1483, https:// gov/citations/20205008200. (Accessed 27 March 2023). doi.org/10.1109/ICRA.2011.5980479. [66] J.D. Giorgini, Status of the JPL horizons ephemeris system, IAU Gen. Assem. 29 [38] S. Koenig, M. Likhachev, A. Incremental, Adv. Neural Inf. Process. Syst. 14 (2002) (2015), 2256293. https://ui.adsabs.harvard.edu/abs/2015IAUGA..2256293G. 1539-1546. https://proceedings.neurips.cc/paper/2001/hash/a591024321c5e2b [67] L. Hawkins, NASA’s initial Artemis human landing system, in: 73rd Int. Astronaut. dbd23ed35f0574dde-Abstract.html. (Accessed 3 April 2023). Congr. No. IAC-22, B3, vol. 1, 2022, X71658, 9, https://ntrs.nasa. [39] S. Koenig, M. Likhachev, A. Incremental, *. InAdvances in Neural Information gov/api/citations/20220012342/downloads/22 9 18 Hawkins HLS IAC final.pdf. Processing Systems, 2002. (Accessed 3 May 2023). [40] D. Ferguson, A. Stentz, Field D*: an Interpolation-Based Path Planner and [68] T. Vicsek, H. Gould, Fractal growth phenomena, Comput. Phys. 3 (1989) 108, Replanner, vol. 28, Springer Tracts Adv. Robot., 2007, https://doi.org/10.1007/ https://doi.org/10.1063/1.4822864. 978-3-540-48113-3_22. [69] D.A. Dickey, W.A. Fuller, Distribution of the estimators for autoregressive time [41] A. Stentz, Optimal and efficient path planning for unknown and dynamic series with a unit root, J. Am. Stat. Assoc. 74 (1979) 427, https://doi.org/10.2307/ environments, Int. J. Robot Autom. 10 (1995) 89–100. https://ieeexplore.ieee. 2286348. org/abstract/document/351061/?casa_token=0uSlmzeHsdwAAAAA:vpzA7K7h 341 E. Peña-Asensio et al. Acta Astronautica 214 (2024) 324–342 [70] R. Johnston, Biomedical Results of Apollo, Scientific and Technical Information [77] M.E. Landis, P.O. Hayne, J.P. Williams, B.T. Greenhagen, D.A. Paige, Spatial Office, National Aeronautics and Space Administration, 1975. distribution and thermal diversity of surface volatile cold traps at the lunar Poles, [71] D.A. Kring, N. Barrett, S. Boazman, A. Gawronska, C. Gilmour, S. Halim, Planet. Sci. J. 3 (2022), https://doi.org/10.3847/PSJ/ac4585. K. McCanaan, A. V Satyakumar, J. Shah, Artemis III EVA opportunities along a [78] J.K. De Witt, W.B. Edwards, M.M. Scott-Pandorf, J.R. Norcross, M.L. Gernhardt, ridge extending from Shackleton crater towards de Gerlache crater, Sci. Defin. The preferred walk to run transition speed in actual lunar gravity, J. Exp. Biol. 217 Team Artemis. (2020) 2042. https://hdl.handle.net/20.500.11753/1709. (2014) 3200–3203, https://doi.org/10.1242/jeb.105684. [72] V.T. Bickel, B. Moseley, E. Hauber, M. Shirley, J.-P. Williams, D.A. Kring, [79] C. Olthoff, EVA walk-back limit calculation using the virtual spacesuit, in: 48th Int. Cryogeomorphic characterization of shadowed regions in the Artemis exploration Conf. Environ. Syst, 2018 ttu-ir.tdl.org/handle/2346/74208%0Ahttps://ttu-ir.tdl. zone, Geophys. Res. Lett. 49 (16) (2022), https://doi.org/10.1029/ org/bitstream/handle/2346/74208/ICES_2018_259.pdf?sequence=1. 2022GL099530. [80] W.C. Liu, B. Wu, An integrated photogrammetric and photoclinometric approach [73] C.I. Fassett, B.J. Thomson, Crater degradation on the lunar maria: topographic for illumination-invariant pixel-resolution 3D mapping of the lunar surface, ISPRS diffusion and the rate of erosion on the Moon, J. Geophys. Res. Planets. 119 (2014) J. Photogramm. Remote Sens. 159 (2020) 153–168, https://doi.org/10.1016/j. 2255–2271, https://doi.org/10.1002/2014JE004698. isprsjprs.2019.11.017. [74] P. Ramachandran, G. Varoquaux, Mayavi: 3D visualization of scientific data, [81] B. Wu, W.C. Liu, A. Grumpe, C. Wöhler, Construction of pixel-level resolution Comput. Sci. Eng. 13 (2011) 40–51, https://doi.org/10.1109/MCSE.2011.35. DEMs from monocular images by shape and albedo from shading constrained with [75] J.D. Hunter, Matplotlib: a 2D graphics environment, Comput. Sci. Eng. 9 (2007) low-resolution DEM, ISPRS J. Photogramm. Remote Sens. 140 (2018) 3–19, 90–95, https://doi.org/10.1109/MCSE.2007.55. https://doi.org/10.1016/j.isprsjprs.2017.03.007. [76] B. Hoffmann, T. Schlotman, L. Cox, J. Somers, Human thermal analysis of traverse [82] K. Mehlhorn, P. Sanders, Algorithms and Data Structures: the Basic Toolbox, and geology tasks during simulated lunar extravehicular activity, in: 2023 IEEE Springer Berlin Heidelberg, 2008, https://doi.org/10.1007/978-3-540-77978-0. Aerosp. Conf, Big Sky, Montana, 2023, pp. 1–8. 342