Lunar rock investigation and tri-aspect characterization of lunar farside regolith by a digital twin

Yutu-2 rover conducted an exciting expedition on the 41st lunar day to investigate a fin-shaped rock at Longji site (45.44°S, 177.56°E) by extending its locomotion margin on perilous peaks. The varied locomotion encountered, especially multi-form wheel slippage, during the journey to the target rock, established unique conditions for a fin-grained lunar regolith analysis regarding bearing, shear and lateral properties based on terramechanics. Here, we show a tri-aspect characterization of lunar regolith and infer the rock’s origin using a digital twin. We estimate internal friction angle within 21.5°−42.0° and associated cohesion of 520-3154 Pa in the Chang’E-4 operational site. These findings suggest shear characteristics similar to Apollo 12 mission samples but notably higher cohesion compared to regolith investigated on most nearside lunar missions. We estimate external friction angle in lateral properties to be within 8.3°−16.5°, which fills the gaps of the lateral property estimation of the lunar farside regolith and serves as a foundational parameter for subsequent engineering verifications. Our in-situ spectral investigations of the target rock unveil its composition of iron/magnesium-rich low-calcium pyroxene, linking it to the Zhinyu crater (45.34°S, 176.15°E) ejecta. Our results indicate that the combination of in-situ measurements with robotics technology in planetary exploration reveal the possibility of additional source regions contributing to the local materials at the Chang’E-4 site, implying a more complicated geological history in the vicinity.

Editorial Note: Parts of this peer review file have been redacted as indicated to avoid any copy right infringement.

REVIEWER COMMENTS
Reviewer #1 (Remarks to the Author): In the manuscript, new observations by/of the Yutu-2 rover and a digital twin are used to estimate the regolith properties within Von Karman crater within the South Pole Aitken (SPA) basin and investigate the composition and origin of the fin-shaped rock near the Longji site.
As written, the manuscript does not provide sufficient details to evaluate the significance of the work and what impact the results from the described analyses will have on the field.Examples of what I mean: (1) The title and text of the manuscript uses the descriptive term comprehensive when describing their analysis of regolith properties, however the authors do not describe what is meant by comprehensive (i.e., are the calculated parameters all the regolith properties you could calculate to fully characterize it?).Additionally, the manuscript does not include uncertainties on the modelled/calculated regolith property measurements to make it clear that the results are a significant contribution to the field.The internal friction angle was determined to be within 21.5 -42.0 degrees and an associated cohesion of 520-3154 Pa, however it is only stated that these numbers make the farside regolith similar to the Apollo 12 soils.Without uncertainties, it is not clear if the manuscript includes significant results for publication.
(2) The inferred source of fin-shaped rock is based on the abundance of minerals derived from MGM and NBSR and comparing those results to derived abundances of minerals from Kaguya MI data.However, the manuscript does not include the uncertainties on these derived abundances and how Yutu-2 in-situ observations can be compared to orbital MI data.How unique is this approach in determining the origin of the rock.Additionally, the manuscript does not discuss the significance of knowing the origin of this rock (i.e., why does it matter that it came from Zhinyu crater rather than Finsen crater) or the significance of this being a lower curst or upper mantle rock.
(3) While equations are provided for the models in the Methods section, inputs into those models were not provided, nor were the assumptions described and how those assumptions and any uncertainties in the inputs play out to errors/uncertainties in the results presented in the paper.Thus, the significance of the results presented in the manuscript are unknown.Examples include: (a) What is the uncertainty on the measurements of things like wheel sinkage from the imaging data?What is the spatial resolution of the imaging data?(b) How are you measuring the size of regolith grains?Particularly at the micron scale?(c) What scientific data, local terrain models and geometric and physical properties were used?What are their uncertainties?(d) Some inputs seem to come from lunar simulants -how accurate are these simulants compared to real lunar regolith?Additionally, much of the paper describes the traverse of the rover as well as previous results from the mission.While this is interesting, it isn't the most scientifically compelling.Another large portion of the paper describes the modeled behavior of the rover -again of limited scientific value as it is written.
Finally, the manuscript is not appropriately referenced as it is missing many of the recent publications on SPA in the past few years.It appears that they are using only references from their team and Chinese colleagues even though much work has been done by scientists from around the world.

Kerri Donaldson Hanna
Reviewer #2 (Remarks to the Author): Using digital twin to infer geotechnical properties of lunar regolith is a very novel approach.In the past, I have seen using wheels to provide geotech properties based on DEM models -see for example

Response to the Comments of Review 1
In the manuscript, new observations by/of the Yutu-2 rover and a digital twin are used to estimate the regolith properties within Von Karman crater within the South Pole Aitken (SPA) basin and investigate the composition and origin of the fin-shaped rock near the Longji site.As written, the manuscript does not provide sufficient details to evaluate the significance of the work and what impact the results from the described analyses will have on the field.Examples of what I mean: Response: Thank you for your comments.Detailed explanation of the uncertainty of input measurements and their effect on the parameter identification results have been added (Response to Comment 1 (2)).We added further analysis of the lunar regolith in terms of the bearing capacity and the bulk density, and more comparison on the shearing property of the lunar regolith at "Longji" site to that in Le Monnier crater has been supplemented to enrich the understanding of its properties (Response to Comment 1 (3)).Significance on the locomotion as well as interaction data present in this study have been emphasized in the revision (Response to Comment 8), and implications on parameter identification results have been discussed (Response to Comment 1 (4)).
Comment 1. 1) The title and text of the manuscript uses the descriptive term comprehensive when describing their analysis of regolith properties, however the authors do not describe what is meant by comprehensive (i.e., are the calculated parameters all the regolith properties you could calculate to fully characterize it?).2) Additionally, the manuscript does not include uncertainties on the modelled/calculated regolith property measurements to make it clear that the results are a significant contribution to the field.3) The internal friction angle was determined to be within 21.5 -42.0 degrees and an associated cohesion of 520-3154 Pa, however it is only stated that these numbers make the farside regolith similar to the Apollo 12 soils.4) Without uncertainties, it is not clear if the manuscript includes significant results for publication.
Response to Comment 1 (1).The comprehensive here means the regolith properties is analyzed and characterized in three aspects, which covers all the aspects (the bearing, shearing and lateral properties) concerned from terramechanics perspective.Admittedly, the word comprehensive may be too strong and not explicit enough to describe our analytical results, thus we substitute it with a milder and more concrete word tri-aspect, and change the title to Digital twin-assisted risky rock investigation and tri-aspect characterization of lunar farside regolith properties accordingly.We have revised the corresponding description in the revision as follows.
(Page 2, lines 3-4) Leveraging digital twin technology, it comprehensively characterized the lunar regolith from three aspects and inferred the rock's origin.
(Page 4, lines 10-12) In this work, we present the risky but successful venture to this peculiar rock enabled by digital twin with associated spectral investigation results, and the tri-aspect property identification of the farside lunar regolith achieved on special slipping and skidding states.
(Page 19, lines 18-20) The tri-aspect parameter identification results presented here serves as a foundational step for subsequent engineering verifications in the lunar farside, such as the assessments of landing feasibility, rover mobility, and sample excavation capabilities.
Response to Comment 1 (2).In terms of modelling, the terramechanics model we used for parameter identification is well established by considers multiple physical effects and well evaluated in previous study.For uncertainty on modelling, we have supplemented additional explanation on the accuracy of models in the Methods section (Page 28, lines 3-6).
These terramechanics models consider the slip sinkage phenomena and the wheellug effect, and could predict the normal force, resistance moment, and drawbar pull with higher accuracy compared to conventional terramechanics models 71 , and their modelling error is less than 10% 40  For uncertainty on measurements, detailed description of uncertainties on measurements for regolith parameter identification have been added in the Methods section as follows (Page 29, lines 16-24; Page 30, lines 1-9).
As explicitly shown in Supplementary Fig. 11, inputs into these models for lunar regolith parameter estimation include forces (FN, FDP, FL), wheel states (slip ratio s, sinkage z, side slip angle β), and wheel parameters (r, b, rs).In this study, the normal force FN, the drawbar pull FDP and the lateral force FL are solved through the constrained dynamics of a multi-rigid-body system with a floating base in the digital twin.The relative errors of estimated forces compared to experimental measurements are within 10% 38,41 , as illustrated in previous studies.The wheel sinkage z is calculated by comparing the elevation difference of the track area and the surrounding surface plane in the reconstructed digital elevation model, which is reconstructed using stereo Navcam images in 1024×1024 pixels.The accuracy of the wheel sinkage measurement is dependent on the accuracy of the single-site DEM, whose topographic data can reach the submillimeter level 73 (i.e., its error is within 1 mm).The wheel slip ratio s is solved with the actual travel distance of Yutu-2 estimated by visual localization and with the planned travel distance by rearranging Eq. ( 6).The accuracy of the slip ratio is dependent on the visual localization yielding an estimation error of 4% 39 .The wheel side slip angle β is estimated using the posture of the rover, and the side slip angle along the forward traverse varied between 0.5° and 3°, whose accuracy depends on the visual positioning and its estimation error is 4% 39 .The remaining rover wheel parameters r and h are constant depending on the rover configuration as listed in Supplementary Table 4, and the equivalent shearing radius rs for Yutu-2's grouser wheel is calculated according to Eq. (2) with lug shearing coefficient of 0.65.The values or ranges of the inputs used in this study are in Supplementary Based on the above uncertainty derived from different sources, we conducted an additional uncertainty analysis of identification results using Monte Carlo simulation.The results as well as analysis have been supplemented in the revision (Page 30, lines 10-24; Page 31, lines 1-10).
In this context, the primary source of error in identification outcomes stems from the measurement uncertainties associated with input variables, including slip ratio, sinkage, side slip angle and interaction forces.Due to the complexity and nonlinearity of our terramechanics models, getting an analytical uncertainty analysis of model output is a difficult task.Therefore, we use Monte Carlo simulations 74 to calculate the uncertainty of model outputs by considering input measurement uncertainties.These measurement errors are represented as normal distributions.The Monte Carlo simulation involves a sample size of 1024, which has been assessed as sufficient for obtaining reliable and robust results 75 .Regarding bearing properties, when we assume a sinkage exponent (N) of 1.0, as the typical value from Apollo missions, the equivalent stiffness (Ks) ranged from 556.7 to 1443 kPa/m N for estimated sinkage of 8-15 mm.In other traverses, wheel sinkage may be smaller but generally not less than 5 mm.For very shallow sinkage, Ks approaches its upper limit with minimal adjustability.Consequently, for a sinkage of 5 mm, Ks was fixed at 1443 kPa/m N .To account for the measurement error associated with wheel sinkage, which was formulated as a normal distribution with a mean of 5 mm and a standard deviation of 0.33 mm (following the three-sigma rule), we conducted Monte Carlo simulations to estimate the corresponding distribution of output sinkage exponent N. The mean of the estimated N value is 0.87 with a standard deviation of 0.017 when only considering sinkage measurement uncertainties.When considering uncertainties in forces (FN, FDP) without accounting for the uncertainty of z (wheel sinkage), the standard deviation of the estimated N is 0.006, indicating that the predicted N is more sensitive to the wheel sinkage errors than to force errors in this case.By considering both uncertainties in forces and wheel sinkage, the standard deviation of the estimated N is estimated to be 0.017, as illustrated in Supplementary Fig. 13(a).For the largest sinkage of 15 mm, the standard deviation of the estimated Ks is approximately 25.8 kPa/m N (Supplementary Fig. 13(b)) when the sinkage exponent N is at the typical value of 1.0.Concerning shear properties, with a slip ratio of -0.075 and accounting for measurement errors on forces and slip ratio, the cohesion was determined to be 520 Pa (the typical values of the lunar regolith), and the internal friction angle φ was estimated to be 21.5° with a standard deviation of 2.29°, as illustrated in Supplementary Fig. 13(c). .

Response to Comment 1 (3).
For longitudinal shear properties, except for showing the similarity to regolith in the Apollo 12 mission, we emphasize the particularity in the increased cohesion for regolith at "Longji" site.Its cohesion was mostly larger than that measured at other sites, which was consistent with the greater soil cohesion phenomenon observed on the wheel.We ready have corresponding descriptions to the enhanced cohesion and further analyzed its implications for geological process they undergo in the manuscript as follows.
(Page 12, lines 23-24; Page 13, lines 1-6) Compared with the lunar regolith properties identified at other nearside landing sites 47 (Fig. 3c), the longitudinal shear property (characterized by cohesion and internal friction angle) of the lunar regolith at "Longji" site was closest to that estimated in the Apollo 12 mission using direct shear method 47 .However, its cohesion was mostly larger than that measured at other sites, which was consistent with the great soil adhesion phenomenon observed on the wheel.The heightened degree of cohesion can be attributed to the increased presence of agglutinates within the lunar regolith, which constitute the principal product of space weathering 48 .Consequently, this may suggest that the local lunar soil is subject to longer periods of exposure and more pronounced space weathering effects, leading to an enhanced level of regolith maturity 48 .48. Tang, Z. et al.Physical and mechanical characteristics of lunar soil at the Chang'E-4 landing site.Geophys.Res.Lett.47, e2020GL089499 (2020).Further analyses on the regolith properties in terms of the bearing capacity have been supplemented to enrich the understanding of farside lunar regolith properties.
(Page 12, lines 6-10) With an average wheel sinkage of 8 mm along the rover's trace, the estimated bearing capacity reached approximately 4 kPa.This value was notably higher compared to the bearing capacity measured along the Lunohkod-1 traverse, where the uppermost layer at a depth of 1 cm exhibited a relatively smaller bearing capacity, falling withing the range of 2-3 kPa 19 .This finding further substantiates the enhanced bearing strength of the lunar regolith at "Longji" site.
Response to Comment 1 (4).With all of these tri-aspect property identification results and added detailed uncertainty analysis, we think the results are a significant supplement for the lunar farside regolith property study, which is lack of data for delicate investigation/analysis.In addition, the locomotion experience and interaction data presented in this study is also valuable for further regolith mechanics studies.They are two of the main contributions of this paper to the field.We have emphasized the significance of the results for regolith mechanics studies and geological implications, and discussed their applications to the terramechanics and space exploration field as follows.
(Page 19, lines 6-9) The experience in locomotion and interaction yields valuable data for regolith mechanics studies, offering insights into how lunar regolith responds to a variety of static and dynamic loadings.This knowledge is essential for the development of terramechanics models that underpin interactions with rovers, landers, scoops, and other vehicles on the lunar surface 19 .
(Page 13, lines 3-6) The heightened degree of cohesion can be attributed to the increased presence of agglutinates within the lunar regolith, which constitute the principal product of space weathering 48 .Consequently, this may suggest that the local lunar soil is subject to longer periods of exposure and more pronounced space weathering effects, leading to an enhanced level of regolith maturity 48 .
(Page 19, lines 15-22) The in-situ identification based on wheel-terrain interaction models with the support of digital twin filled the gaps of the shear property estimation of the lunar farside regolith, and also provided a promising method to infer lateral properties of the regolith in extraterrestrial environments with initial parameters.The tri-aspect parameter identification results presented here serves as a foundational step for subsequent engineering verifications in the lunar farside, such as the assessments of landing feasibility, rover mobility, and sample excavation capabilities.Moreover, these findings may have implications for future in situ resource utilization ( Comment 2. The inferred source of fin-shaped rock is based on the abundance of minerals derived from MGM and NBSR and comparing those results to derived abundances of minerals from Kaguya MI data.However, the manuscript does not include 1) the uncertainties on these derived abundances and 2) how Yutu-2 in-situ observations can be compared to orbital MI data.3) How unique is this approach in determining the origin of the rock.4) Additionally, the manuscript does not discuss the significance of knowing the origin of this rock (i.e., why does it matter that it came from Zhinyu crater rather than Finsen crater) or the significance of this being a lower curst or upper mantle rock.
Response to Comment 2 (1).We have provided the error of the MGM estimation method in the original Fig. 4c, which is 0.267%.This is also the error in derived mineral abundances.We have added this point in the main text in the revised manuscript (Page 17, lines 13-15).
Note that the fitting error for the MGM method was 0.267% and since plagioclase was not included in the MGM methods, only relative abundance of mafic olivine, OPX and CPX were compared with the orbiter-derived data.
Response to Comment 2 (2)(3).It is a standard operation to trace the origins of rocks observed in situ to their source regions using the orbiter-derived data, particularly when there is a lack of in-situ observations or sample-returned analysis of the potential source regions.Yes, indeed, as the reviewer has pointed out, orbital-derived and in situderived spectral data are difficult to directly compare because of their difference in spatial scales, such as 100s or 1000s meter-scale versus centimeter-scale.However, if the mineralogy of the in-situ detection shows strong similarity to the spectra of in situ measurements, one can infer with greater confidence that the two spatial-scale observations are in agreement with each other 23 ; otherwise, additional data, both in situ and from orbital, would be necessary to conclude.In our case, the in-situ observation data are in good agreement with previous in-situ measurements of other rock targets, and it is also consistent with the derived mineralogical compositions of the Zhinyu crater.Therefore, here we conclude that the Fin-rock shares a similar origin with other previously studied rock targets along the traverse and ejecta from the Zhinyu Crater rather than the Finsen crater.We have discussed the limitation of such comparison with data derived from different spatial scale measurements in the relevant parts in the In situ spectral investigation of the target rock section.
(Page 17, lines 10-21) The abundances of minerals (i.e., olivine, OPX, and CPX), as indicated by the mosaic map created from topographically corrected Mineral Mapper reflectance data from the Kaguya MI, is similar to the modal mineralogy of ejecta from Zhinyu crater (Supplementary Table 3).Note that the fitting error for the MGM method was 0.267% and since plagioclase was not included in the MGM methods, only relative abundance of mafic olivine, OPX and CPX were compared with the orbiter-derived data.We understand that orbital-derived and in-situ-derived spectral data are difficult to compare due to the difference in spatial scales directly; however, because the in situ spectra suggest the fin-shaped rock is consistent with previously investigated rock targets along the traverse and in agreement with the derived mineralogical compositions of the Zhinyu crater, we infer that the target boulder belongs to the Zhinyu crater ejecta rather than those of the Finsen crater.Further investigations along the traverse of the Yutu-2 rover and potentially other sample-returned missions would be required to constrain the precise source regions of the local rocks.Response to Comment 2 (4).We have expanded one paragraph in Discussion section to emphasize the scientific significance in determining the source region of the Fin-shaped rock (Page 20, lines 1-15).
The fin-shaped rock was homologous in spectral parameters to six rocks investigated previously in the Chang'E-4 mission and inferred to be sourced from the Zhiyu crater ejecta based on its relative abundance of 'OL-OPX-CPX' assemblages.This is the second large rock fragment inferred to be ejected from the Zhinyu crater along the traverse of the Yutu-2 rover.Zhinyu crater is a relatively young impact crater located about 30 km west of the landing site 58 .The rover had closely investigated A previous rock fragment on the third lunar day and concluded it originated from the Zhinyu crater 23 .Therefore, our discovery of the lastest rock piece originated from Zhinyu cater supports that besides the majority of ejecta blanket from the Finsen crater to the CE-4 landing site, other source regions may also contribute to the local materials, suggesting a more complicated geological history in the local area.Meanwhile, the finshaped rock is also dominant by plagioclase, consistent with the previous suggestions that the CE-4 region mainly sampled the mare basalt instead of deeper mantle materials 58 .These in-situ observations provide important ground truth for remote sensing investigation of the region and lay an essential foundation for reconstructing the thermal evolution history of the regional mare activities, and provide a better understanding of the geological context of SPA and the compositions of the lunar dichotomy at the farside, as well as the upcoming CE-6 sample-return mission 59  Comment 3.While equations are provided for the models in the Methods section, 1) inputs into those models were not provided, 2) nor were the assumptions described 3) and how those assumptions and any uncertainties in the inputs play out to errors/uncertainties in the results presented in the paper.Thus, the significance of the results presented in the manuscript are unknown.

Response to Comment 3 (1).
As mentioned in the Response to Comment 1 (2), additional explanation regarding inputs into models with associated uncertainties have been added in the revision.
Response to Comment 3 (2) Thanks for the valuable suggestion.We have added the model assumption at the end of the corresponding Method section as follows (Page 28, lines 6-9).
The bearing model (Eq.(1a)) is adopted from Bekker model 72 with semi-empirical equations, thus it is based on the assumption that the wheel slip ratio is no larger than 0.6 67 .For high slippery (s>0.6)cases, the accuracy of the above semi-empirical terramechanics models will get significantly affected, and cannot reach a reasonable agreement with the wheel mobility performance.67.Ding, L. Wheel-Soil Interaction Terramechanics for Lunar/Planetary Exploration Rovers: Modeling and Application.PhD thesis, Harbin Institute of Technology (2009).72.Bekker, M. G. Off-the-road-locomotion (Ann Arbor, MI: The University of Michigan Press, 1960).
Response to Comment 3 (3) For assumptions, additional explanation on the model applicability in our case has been added in the revision (Page 28, lines 9-14).
In this study, the rover wheel work on skid condition during the outbound traverse, and most the wheel slip ratios are between 0 and -0.075 and no less than -0.1, satisfying the slip ratio assumption and can be applied to parameter identification.When the slip ratio is over 0.6, the parameter identification process can still obtain a set of parameters in the sense of fitting, but the model is no longer in high accuracy in such condition, thus the accuracy of the identified parameter is also affected.
For inputs uncertainties, as mentioned in the Response to Comment 1 (2), we have added additional uncertainty analysis on identification results based on Monte Carlo simulations.

Examples include:
Comment 4 (a) What is the uncertainty on the measurements of things like wheel sinkage from the imaging data?What is the spatial resolution of the imaging data?
Response to Comment 4. The accuracy of the wheel sinkage measurement is dependent on the accuracy of the single-site digital elevation model (DEM) reconstructed from Navcam images, whose topographic data reaches the submillimeter level.The spatial resolution of the Navcam imaging data is 1024×1024 pixels.Except for the wheel sinkage z, other measurements involved in regolith parameter identification are wheel slip ratio s and side slip angle β.The accuracy of wheel slip ratio s is dependent on visual localization yielding an estimation error of 4% 39 .The side slip angle β is estimated with the posture of the rover, whose estimation error is 4% 39 .Details about measurement uncertainties for regolith parameter identification have been added in the 'Lunar regolith parameter estimation at the "Longji" site' subsection as follows (Page 29, lines 21-24; Page 30, lines 1-6).
The wheel sinkage z is calculated by comparing the elevation difference of the track area and the surrounding surface plane in the reconstructed digital elevation model, which is reconstructed using stereo Navcam images in 1024×1024 pixels.The accuracy of the wheel sinkage measurement is dependent on the accuracy of the single-site DEM, whose topographic data can reach the submillimeter level 73 (i.e., its error is within 1 mm).The wheel slip ratio s is solved with the actual travel distance of Yutu-2 estimated by visual localization and with the planned travel distance by rearranging Eq. ( 6).The accuracy of the slip ratio is dependent on the visual localization yielding an estimation error of 4% 39 .The wheel side slip angle β is estimated using the posture of the rover, and the side slip angle along the forward traverse varied between 0.5° and 3°, whose accuracy depends on the visual positioning and its estimation error is 4% 39  Measurements used for rock identification include the visible and near-infrared (VNIR) hyperspectral images and single-pixel short-wave infrared (SWIR) spectra from the VNIS instrument.The measurement uncertainties are 5% and 7% for VIS/NIR and SWIR, respectively.We further claimed the uncertainty of the scientific data used in this study at the end of the "Instruments and data description" section as follows (Page 23, lines 11-12).
The measurement uncertainties are 5% and 7% for VIS/NIR and SWIR, respectively 65  Comment 5. How are you measuring the size of regolith grains?Particularly at the micron scale?
Response to Comment 5.The size of the regolith grains was estimated from the image.We have removed "microto millimeter-sized" from the original manuscript due to the lack of a reference scale for this image.A fine-grain regolith was a consensus for the grains attached to the rock surface.Comment 6.What 1) scientific data, 2) local terrain models and geometric and physical properties were used?What are their uncertainties?
Response to Comment 6 (1).The scientific data used in this study includes Pancam images, the visible and near-infrared (VNIR) hyperspectral images and singlepixel short wave infrared (SWIR) spectra from the VNIS instrument.Images from Pancam are 2352×1728 pixels in color mode or 1176×864 pixels in panchromatic mode as illustrated in Supplementary Table 5.The visible and near-infrared (VNIR) hyperspectral images are 256×256 pixels as illustrated in Supplementary Table 6.The measurement uncertainties are 5% and 7% for VIS/NIR and SWIR, respectively.We further claimed the scientific data used in this study with its measurement uncertainty in the Instruments and data description section as follows.
(Page 22, lines 17-19) The data used in this study include images from a Pancam, Navcam, and two HazCams, alongside the visible and near-infrared (VNIR) hyperspectral images and single-pixel short-wave infrared (SWIR) spectra from the VNIS instrument.
(Page 22, lines 20-22) Pancam is one of the scientific payloads used primarily for high-resolution mapping and localization.It is mounted on the mast of the Yutu-2 rover, consisting of two optical systems of identical functions, performances, and interfaces, parameterized as Supplementary Table 5.
(Page 23, lines 6-12) The VNIS 65,66 is composed of a complementary metaloxide-semiconductor (CMOS) image with 256 by 256 pixels, a SWIR spectrometer, and a white panel for calibration and dust-proofing.It is assembled on the anterior of Nomenclature Meaning the rover to detect the composition of the lunar surface materials at a fixed 45° zenith angle at a height of 0.69 m.Its spectral wavelength ranges are 450-945 nm and 900-2395 nm with a default sampling interval of 5 nm.For the SWIR spectrometer, its field of view is a circular area in the CMOS image centered at (96, 128) with a 54 pixel radius (Supplementary Table 6).The measurement uncertainties are 5% and 7% for VIS/NIR and SWIR, respectively 65 12, the DEMP 2 is separated into discrete nodes and triangle elements, and each node has its own physical properties.The coordinates of terrain nodes are given as (x, y, z, Ks, N, c, φ, Kx, φy, Ky), in which (x, y, z) represent 3-dimensional position of the node in inertial frame, i.e., geometric properties, and (Ks, N, c, φ, Kx, φy, Ky) are physical properties of the node.The local terrain model of the "Longji" site was reconstructed with 0.02m spatial resolution based on Pancam stereo images 39 , and its raw geometric properties represented in elevation map is shown in Supplementary Fig. 1a.The topographic data from the single-site DEM reaches the submillimeter level 73 .In the simulation, the physical properties to be identified are under determined, and set in a wide range of parameters to cover most cases, while non-dominant physical parameters are set as the typical value of the lunar regolith from Apollo data 47 , as listed in Supplementary Table 8. 41 is a lunar regolith simulant which is equivalent to FJS-1 81 , whose material components and mechanical characteristics are similar to those of the real lunar soil 47 , as listed in Supplementary Table S1 and 11.The simulants from ref. 82 is made from standard commercial experimental sand, numbered HIT-LSS2, whose particle size is set to be uniform so that the repeatability of the sand is secured.Its physical and mechanical property parameters are listed as Supplementary Tabel 12.

Supplementary Fig. 12 Description of the DEMP 2 used in the dynamic simulation
We have added additional explanation of the accuracy of these simulants compared to real lunar regolith in the revision as follows (Page 15, lines 11-16).
The lunar simulant is equivalent to FJS-1 81 , whose material components and mechanical characteristics (Supplementary Table 11) are similar to those of the real lunar soil, as reported in ref. 47.Another simulant (Supplementary Table 12) is standard commercial experimental sand, numbered HIT-LSS2, whose particle size is set to be uniform for repeatability of terramechanics experiments.The lateral parameters of the lunar simulant and the standard commercial experimental sand are from ref. 41  Supplementary Table 13 The physical and mechanical parameters of the lunar soil simulant and HIT-LSS2 82, 85 ρ (Kg/m 3 ) kc (kPa/m n-1 ) kφ Lunar soil simulant 42 HIT-LSS2 Note: ρ is bulk density, kc is cohesion modulus of the soil, kφ is the frictional modulus of the soil, n is the sinkage exponent, c is the cohesion of the soil,  is the internal friction angle of the soil, Kx is the longitudinal shearing deformation modulus of the soil, Ky is the lateral shearing deformation modulus of the soil.41.Ishigami, G., Miwa, A., Nagatani, K., Yoshida, K. Terramechanics-based model for steering maneuver of planetary exploration rover on loose soil.J. Field Robot.24, 233-250 (2007).47.French, B. M., Heiken, G., Vaniman, D., Schmitt, H. H., & Schmitt, J. Lunar Sourcebook A Users Guide to the Moon (Cambridge Univ.Press, 1991).81.Kanamori, H., Udagawa, S., Yoshida, T., Matsumoto, S., Takagi, K., Properties of lunar soil simulant manufactured in Japan.In the 6 th  as well as previous results from the mission.While this is interesting, it isn't the most scientifically compelling.2) Another large portion of the paper describes the modeled behavior of the roveragain of limited scientific value as it is written.

Response to Comment 8 (1).
Thank you for the comments.We have further emphasized the significance on rover traverse analysis and discussed its impact on other studies in the revision.
(Page 5, lines 7-16) Such robotic geological exploration to desired scientific interesting target relies significantly on the successful traversal of rovers across diverse extraterrestrial terrains.However, from the locomotion perspective, this potential traverse was full of mobility hazards and uncertainties.On the one hand, the Yutu-2 rover was likely to suffer highly risky wheel skidding 30 when moving downwards on such a slope.Furthermore, uncontrollable lateral slippage would inevitably occur with broken nonholonomic constraints of the rover during the traverse, thus the pathfollowing accuracy of Yutu-2 is hard to guarantee.Locomotion failures on harsh or slippery terrains have ever brought serious consequences, such as reduced tractive performance, deviation from planned trajectories, and in the worst-case scenario, becoming immobilized and permanently trapped, exemplified on previous missions on the Moon (like Lunar Roving Vehicle (LRV) 32 , Luna 21 and Lunokhod 2 33 ) and Mars exploration missions 34,35 .
(Page 5, line 24; Page 6, lines 1-4) To keep the mission continue, movements on harsh terrains with slipping risk must be justified to remain within the acceptable bounds of the rover's mobility safety margin prior to execution.
(Page 19, lines 6-9) The experience in locomotion and interaction yields valuable data for regolith mechanics studies, offering insights into how lunar regolith responds to a variety of static and dynamic loadings.This knowledge is essential for the development of terramechanics models that underpin interactions with rovers, landers, scoops, and other vehicles on the lunar surface 19

Response to Comment 8 (2).
Additional statistical analysis on the behavior modelling error has been added to strengthen the prediction results; the significance of accurate behavior modelling for rover mobility prediction and mission success has been further stressed; and the hidden philosophy of digital twin exemplified by behavior modelling and its insight into broad engineering and scientific problems have been discussed in the revision.
(Page 9, lines 13-16) The lateral model employed for representing wheel side force underwent rigorous validation to enhance its predictive performance for steering trajectories, achieving a final state error of less than 15% 41 .Additionally, this model exhibits a high degree of accuracy in estimating the rover's orientation 41 .
(Page 9, lines 21-23) The small discrepancy between the predicted state and the real-world state underscores the robustness and efficacy of the digital twin system, uniquely positioned to enhance decision support and elevate the mission success rate.
(Page 19, lines 4-6) Precise locomotion simulation and thorough pre-traverse evaluation significantly mitigate the risks of mission failure by meticulously modeling wheel-terrain interactions and leveraging real-world data.
(Page 14, lines 4-9) The elaborate wheel-regolith interaction models, adaptable to various motion conditions, constitute the cornerstone for predicting the rover's realistic mobility behavior within the digital twin system, while the real-world data is used to update the models towards higher fidelity.The high integration of models and data within the digital system exemplified by behavior prediction demonstrate the system's remarkable capability to bridge the gap between simulation and reality, with broad implications for other sim2real challenges.41.Ishigami, G., Miwa, A., Nagatani, K., Yoshida, K. Terramechanics-based model for steering maneuver of planetary exploration rover on loose soil.J. Field Robot.24, 233-250 (2007).

Comment 9.
Finally, the manuscript is not appropriately referenced as it is missing many of the recent publications on SPA in the past few years.It appears that they are using only references from their team and Chinese colleagues even though much work has been done by scientists from around the world.
Response to Comment 9. Thank you for this valuable feedback.In this revision, we have prepared a separate paragraph reviewing the SPA studies conducted by international contributors besides the Yutu-2 team and included more literature in this paragraph.In the first paragraph of the Introduction, we have also added two papers led by the international groups to provide a more balanced overview of the study context.
(Page 2, lines 18-22) As the oldest and largest impact basin on the Moon, the South Pole-Aitken (SPA) basin is one of the most appealing farside places that is supposed to have exposed the lunar lower crust and probably upper mantle materials 3,4 , and promising to reveal the indeterminate evolution of the early Moon with oldest mare basalts ever detected 5,6 .
(Page 3, lines 3-16) Estimates of lunar crustal thickness obtained from the GRAIL mission corroborate the notion that the SPA impact event likely excavated materials deep into the mantle 8 , and there presents a large excess of mass in the lunar mantle under the SPA 9 .Additional evidence from remote sensing, impact modeling, and geological analyses indicates that the SPA impact ejected ilmenite-bearing cumulates (IBCs) and KREEP-bearing rocks from the uppermost mantle 10,11 .Continuous spectral reflectance data acquired by the Spectral Profiler instrument aboard the lunar explorer

Response to the Comments of Review 2
Comment 1.Using digital twin to infer geotechnical properties of lunar regolith is a very novel approach.In the past, I have seen using wheels to provide geotech properties based on DEM models -see for example Johnson et al., Discrete element method simulations of Mars Exploration Rover wheel performance, J of Terramechanics, Volume 62, December 2015, Pages 31-40 Response to Comment 1.We greatly appreciate the reviewer's positive comments and constructive suggestions to help us improve the manuscript.Thanks for sharing the reference using discrete element method for micro-scale properties study, which was a great supplement for the microscopic properties investigated in this work.We have added it in the discussion as follows.
(Page 20, lines 19-21) In addition to the macroscopic properties of the lunar soil, its microscopic properties are also worth an in-depth examination, which can be achieved through discrete element-based wheel-regolith interaction simulations 60  Response to Comment 2. The lateral properties of the lunar regolith characterize the lateral force on the wheel during the wheel-terrain interaction when the wheel has a lateral travelling velocity vy.The properties are parameterized by external friction angle φy and the lateral shearing deformation modulus of the soil Ky, except for the cohesion c.
When the forward velocity of the wheel v deviates from its heading direction vx due to the existence of lateral travelling velocity vy, the wheel is subjected to an additional lateral resistance force FL acting along the lateral direction of the wheel to resist this lateral movement.The lateral resistance force FL is integrated by the lateral shear stress τy, and the soil lateral properties are parameters characterizing the lateral force or lateral shear stress of the wheel during the wheel-terrain interaction.According to the ref.41, the soil lateral properties are parameterized by the cohesion c, external friction angle φy and the lateral shearing deformation modulus of the soil Ky in the lateral shear stress model, similar to the representation of the longitudinal shear properties characterized by cohesion c, internal friction angle φ and the longitudinal shearing deformation modulus Kx.The external friction angle φy represents the roughness between the wheel surface and the soil, and the lateral shearing deformation modulus of the soil Ky represents the tangential shear strength of the soil.We explained the definition of lateral properties in the revision (Page 13, lines 8-13).
The lateral properties of the lunar regolith characterize the lateral force on the wheel during the wheel-terrain interaction when the wheel has a lateral travelling velocity vy.The properties are parameterized by the external friction angle φy and the lateral shearing deformation modulus of the soil Ky.The external friction angle φy represents the roughness between the wheel surface and the regolith, and the lateral shearing deformation modulus of the soil Ky represents the tangential shear strength of the regolith.
Additional summation of all three aspects of soil properties has been added at the end of the wheel-terrain interaction modelling section in Methods (Page 27, line 16-19; Page 28, lines 1-2).
In our models, the terrain mechanical parameters are characterized in bearing, longitudinal shearing and lateral shearing three aspects.The bearing properties are related to the bearing strength of the soil represented in Ks and N; while the shearing properties regarding soil shear strength are characterized in the longitudinal and tangential directions.They are symbolized by c, φ, Kx and φy, Ky, respectively.The external friction angle φy represents the roughness between the wheel surface and the soil, and the lateral shearing deformation modulus Ky represents the tangential shear strength of the soil.41.Ishigami, G., Miwa, A., Nagatani, K., Yoshida, K. Terramechanics-based model for steering maneuver of planetary exploration rover on loose soil.J. Field Robot.24, 233-250 (2007).
Response to Comment 3. The definition of 'lateral shearing deformation modulus' is the soil deformation modulus in lateral direction 42 .The soil shear deformation modulus K is equivalent to a time constant of the stress-deformation curve, and the value of K is defined by the interaction mechanics between wheel and soil.The shear deformation modulus K can be divided into longitudinal and lateral directions symbolized by Kx and Ky respectively, and they are empirically estimated as functions of slip angle β.
We added the corresponding definition where the lateral shearing deformation modulus appeared for the first time in the text as follows (Page 8, line 18-21) and the nomenclature sheet in the supplementary as well.
A wide range of parameters for regolith was set in the wheel-terrain interaction model to cover most cases, e.g., the internal friction angle φ varied from 25° to 55°, and the lateral shearing deformation modulus Ky (the soil deformation modulus in lateral direction 42 ) was within the range of 15 to 45 mm.Response to Comment 4. The skid condition is the negative slip condition when the circumference velocity of wheel is smaller than the traveling velocity of wheel.We have added the definition of the 'skid condition' in the revision (Page 9, lines 2-5).
During the outbound journey, simulation results (Supplementary Fig. 5) show that rover wheels work mostly in skid condition (a negative slip condition when the circumference velocity of wheel is smaller than the traveling velocity of wheel), and suffer lateral slippage to a certain extent.
In addition, we have added the description of 'slip condition' as well to distinguish the difference between those two conditions (Page 25, lines 12-13).
If s>0, the wheel is in slip condition; if s=0, the wheel rolls without slipping and skidding; and if s<0, the wheel is in skid condition.leveraged the three-dimensional discrete element method (DEM) simulations of wheel drawbar pull and sinkage to determine the particle packing density (0.62) and the interparticle friction coefficient (0.8) with MIT MER wheel performance testing data.These geotechnical properties investigated in this reference are the micro-scale properties of the soil related to the interparticle interaction only under longitudinal motion, while the soil properties studies in this work are macro-scale properties concerned in the wheel-soil interaction under both longitudinal and steering motion.The micro-scale properties of the soil presented in the reference is a great complement to our work, but there is no lateral property of the regolith illustrated and no in-situ results.Therefore, to our best knowledge, our work is still the first to investigate the lateral property of the lunar regolith via in-situ measurements.
We have added the suggested reference as future research direction towards microscale properties using the discrete element method in the discussion.
(Page 20, lines 19-21) In addition to the macroscopic properties of the lunar soil, its microscopic properties are also worth an in-depth examination, which can be achieved through discrete element-based wheel-regolith interaction simulations 60  Response to Comment 8 (1).Yutu-2 is similar in suspension configuration to NASA MER, MSL and Mars 2020.All of them use the rocker-bogie suspension that connects the six wheels to the body of the rover with three main components: differential, rocker and bogie.The differential mechanism of Yutu-2 is inside the body, which is similar to the counterpart of MER, but different from MSL and Mars2020, whose differential mechanism are outside of the body connecting to the left and right Fig 3, 4 and others are too small.Pls increase the size.

Supplementary Fig. 13
Uncertainty of the estimated mechanical properties using Monte Carlo simulations.a, Distribution of estimated sinkage exponents considering the measurement error of wheel sinkage and interaction forces.The results are conditioned on wheel sinkage of 5 mm with the standard deviation of 0.33 mm, and normal force of 32.027 N with 10% uncertainty, and drawbar pull of -1.33 N with 10% uncertainty.The mean of the sinkage exponent is 0.87 with standard deviation of 0.017.b, Distribution of estimated equivalent stiffness considering the measurement error of wheel sinkage and interaction forces.The results are conditioned on wheel sinkage of 15 mm with standard deviation of 0.33 mm, and the same force error as (a).c, Distribution of estimated internal friction angles considering the measurement error of slip ratio and force uncertainty.The results are conditioned on slip ratio of -0.075 with 4% uncertainty.The forces are in the same setting as (a).74.Mooney, C. Z. Monte carlo simulation (New Delhi, London: SAGE Publications, 1997).75.Zhou, R. Y. et al.Sensitivity analysis and dominant parameter estimation of wheelterrain interaction model.Acta Aeronautica et Astronautica Sinica 42, 524076 23. Ma, P. et al.A plagioclase-rich rock measured by Yutu-2 rover in Von Karman crater on the far side of the Moon.Icarus 350, 113901 (2020).
. 65. Li, C. et al.Chang'E-4 initial spectroscopic identification of lunar far-side mantlederived materials.Nature 569, 378-382 (2019).66. He, Z. et al.Spectrometers based on acousto-optic tunable filters for in-situ lunar surface measurement.J. Appl.Remote Sens. 13, 027502 (2019).Response to Comment 6 (2).The local terrain model with geometric and physical properties used in this study is a digital elevation model (DEM) with physical properties named DEMP 2 proposed from ref. 38.Additional explanation of the local terrain model with geometric and physical properties with modeling accuracy and parameter settings have been added in the revision (Page 33, lines 12-22).The local terrain model with geometric and physical properties used in this study is a digital elevation model (DEM) with physical properties named DEMP 2 proposed from ref. 38.As shown in Supplementary Fig.

Comment 5 .Comment 6 .
Page 10, Line 180: spelling: variables and not varibles Response to Comment 5. Revised.Page 10, Line 193: see Johnson et al. above Response to Comment 6. Thanks for sharing the reference.Johnson et al.
. 60. Johnson, J. et al.Discrete element method simulations of Mars Exploration Rover wheel performance, J. Terramech.62, 31-40 (2015).Comment 7. Fig 3, 4 and others are too small.Pls increase the size.Response to Comment 7. Thank you for this point.We have enlarged and reformatted Fig. 3, 4 and others (like Supplementary Fig. 10) according to the journal image formatting requirements.Comment 8. 1) Page 16, Line 294: How is Yutu-2 suspension different from NASA MER, MSL, and Mars2020?If it's the same, please state that.If it's differentpls state how.2) Also -what was the reason for selecting this as opposed to other mobility architectures?

Fig. 11. Regolith parameter estimation. Parameters
in gray box are input of the framework, and they are fixed parameters set according to wheel parameters or obtained by the dynamic solution or external measurements.Equations in the orange boxes are key equations for parameter identification.Parameters in blue box are the output of the framework and are specific to terrain bearing, shearing and lateral parameters.

Supplementary Table 7 Inputs values of the wheel-terrain interaction models for parameter identification
ISRU) technologies, where lunar regolith plays a pivotal role in base construction, mining, and resource extraction.19.Slyuta, E. N. Physical and mechanical properties of the lunar soil (a review).

Table S2 Nomenlature
Ks equivalent stiffness modulus of the soil N variable sinkage exponent of the wheel-terrain interaction c cohesion of the soil

Table 8 . Setting of the terrain mechanical parameters in the simulation
Landing site topographic mapping and rover localization for Chang'E-4 mission.Sci.China Inf.Sci.63, 140901 (2020).47.French, B. M., Heiken, G., Vaniman, D., Schmitt, H. H., & Schmitt, J. Lunar Sourcebook A Users Guide to the Moon (Cambridge Univ.Press, 1991).73.Tang, Z. et al.Physical and mechanical characteristics of lunar soil at the Chang'E-4 landing site.Geophys.Res.Lett.47, e2020GL089499 (2020).Due to lack of lateral property data measured with real lunar regolith, we had to compare our identification results with the released lateral parameters of lunar simulants.These two kinds of simulant samples that we used for lateral parameter comparison are derived from ref. 41 and ref. 82.The simulants from ref.
Comment 7. (d) Some inputs seem to come from lunar simulantshow accurate are these simulants compared to real lunar regolith?Response to Comment 7.

Table 12 Mechanical properties of Apollo samples and simulants 81
and 82.
International Conference and Exposition on Engineering, Construction, and Operations in Space (1998).82.Li, J. Research on wheel soil interaction mechanics for planetary exploration rovers under cornering and slip conditions.Master thesis, Harbin Institute of Technology (2017).85.Ding, L. et al.Experimental Study and Analysis of the Wheels' Steering Mechanics for Planetary Exploration WMRs Moving on Deformable Terrain.Int.J. Robot.Res.