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Do Earth-Trained Humanoid Controllers Walk on the Moon? Gravity, Terrain, and Soil Transfer

Guillem Casadesus Vila, Sri Aditya Deevi, Grace X. Gao

arXiv:2610.30080v1cs.RO

TL;DR

Prior learned-locomotion studies mostly treated reduced gravity on rigid ground or granular terrain at Earth gravity, leaving humanoid performance across both conditions and Earth costs of lunar adaptation open. The authors train 12 G1 policies varying gravity, terrain, and rigid or 3D RFT contact, then test them across gravities and held-out soil models alongside frozen SONIC. Gravity transfer is asymmetric: Earth-trained policies retain only part of survival at the Moon, Moon-trained and fine-tuned policies cannot stand at Earth, and rough 3D RFT gravity randomization maintains seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on every key test cell up to 20°.

  • Problem

    Prior learned-locomotion studies mostly treated reduced gravity on rigid ground or granular terrain at Earth gravity, leaving humanoid performance across both conditions and Earth costs of lunar adaptation open.

    Source: §I · p. 1

  • Method

    The authors train 12 G1 policies varying gravity, terrain, and rigid or 3D RFT contact, then test them across gravities and held-out soil models alongside frozen SONIC.

    Source: §I · p. 1

  • Results

    Gravity transfer is asymmetric: Earth-trained policies retain only part of survival at the Moon, Moon-trained and fine-tuned policies cannot stand at Earth, and rough 3D RFT gravity randomization maintains seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on every key test cell up to 20°.

    Source: §I · p. 1, §VI · p. 9

  • Takeaways & Limitations

    The soil progress ratio ρv compares mean signed soil progress with the same engine’s rigid-run progress on matching geometry and starts; values above 1 indicate greater soil progress.

    Source: C. Evaluation Protocol and Metrics · p. 5

    All results are simulations for one robot, and no ground test applies lunar gravity to a robot and soil together.

    Source: §VI · p. 9

Abstract

from arXiv · show

The Moon changes gravity, terrain, and soil at once. Learned locomotion has studied reduced gravity on rigid ground and granular terrain mostly at Earth gravity, but not humanoids under both, generalist-controller transfer, or the Earth cost of lunar adaptation. On a simulated Unitree G1, we train 12 policies with one recipe, varying gravity, terrain geometry, and ground contact (rigid or three-dimensional resistive force theory, 3D RFT), and including Earth-to-Moon fine-tuning and gravity randomization. We test them at both gravities on rigid ground and 3D RFT, and at their training gravity on three held-out soil models. We also test the frozen SONIC, a released generalist humanoid controller, at both gravities on rigid ground only. Gravity transfer is asymmetric. Earth-trained policies keep 0.64 to 0.75 survival at the Moon on flat rigid ground, Moon-trained and fine-tuned policies cannot stand at Earth, and SONIC survives at most 0.10 at the Moon. Rough training lifts combined-tile survival from 0.53 to 0.98 at Earth and 0.80 to 0.99 at the Moon. In 3D RFT, soil training helps on Earth sand, on tiles and for rough-trained policies also on flat sand. On the stiffer lunar soil it helps only flat-trained Earth policies at Earth and changes the survival of Moon-trained policies by at most a few hundredths. In the sampled rollouts of the held-out soil models, Moon-trained policies keep most of their rigid-ground progress on lunar regolith at the low G1 foot pressure, with per-seed progress ratios of 0.84 to 1.39 apart from one seed with a short rigid reference. A gravity-randomized policy trained on rough 3D RFT terrain has a seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on every key test cell up to 20 degrees. Lunar results are simulation predictions conditional on the contact model and soil stiffness.

I. INTRODUCTION

Lunar locomotion combines reduced gravity, changing footholds, and yielding regolith, while prior learned-locomotion work largely treated these conditions separately. The study compares humanoid-controller transfer and adaptation strategies across those conditions, including their Earth performance.

Research gap

  • Prior work mostly adapted task-specific recipes to reduced gravity on rigid ground or granular media at Earth gravity, leaving humanoids under both conditions understudied.The introduction also identifies missing tests of generalist-controller transfer and of the Earth cost of lunar adaptation.Source: §I · p. 1

Study design

  • The study trains 12 G1 policies across gravity, terrain geometry, and rigid or 3D RFT ground, and evaluates SONIC as a frozen reference.The design includes training from scratch, Earth-to-Moon fine-tuning, and gravity randomization.Source: §I · p. 1

Evaluation scope

  • The paper evaluates rough-terrain and 3D RFT soil training on held-out terrain, slopes, and soils.It also evaluates three soil models held out of training: MPM, SCM, and CRM.Source: §I · p. 1

Training strategies

  • The rough 3D RFT gravity-randomized policy has seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on every key test cell up to 20°.The contribution frames this as a comparison of training from scratch, fine-tuning, and gravity randomization for the Moon.Source: §I · p. 1

II. RELATED WORK

Prior work established learned humanoid locomotion and adaptation on Earth, alongside reduced-gravity and planetary locomotion studies in other settings. This paper extends that context by studying a G1 across gravity, terrain, and ground conditions and testing whether lunar adaptation preserves Earth walking.

A. Humanoid Controllers and Adaptation

  • Randomizing simulator parameters is described as a standard robustness approach, while fine-tuning can erase earlier skills through catastrophic forgetting.Training across Earth and lunar gravity applies randomization to the Moon setting.Source: A. Humanoid Controllers and Adaptation · p. 2
  • SONIC’s motion-tracking controller was trained on about 700 hours of motion capture and connects to navigation through a real-time kinematic planner.The authors compare complete controllers because SONIC’s references, observations, and pretraining differ from those of the velocity policy.Source: A. Humanoid Controllers and Adaptation · p. 2

B. Reduced-Gravity and Planetary Legged Locomotion

  • Earlier reduced-gravity legged-robot studies include hopping, jumping, and quadrupedal walking, while one G1 study compared an Earth baseline with lunar fine-tuning and training from scratch.The present study trains across gravity, terrain, and ground with one recipe and three seeds, and tests whether Moon-adapted policies still walk on Earth.Source: B. Reduced-Gravity and Planetary… · p. 2

C. Granular Contact and Prediction Credibility

Granular locomotion work provides methods for modeling and testing soil contact, but the gravity dependence of granular resistance remains unsettled. The study therefore compares policy outcomes across soil models rather than asserting which model best represents lunar regolith.

C. Granular Contact and Prediction Credibility

  • Prior granular-locomotion research includes 3D RFT G1 training with checks in MPM and on basalt, dry sand, and beach sand.Other cited work combines granular simulation with adaptive quadrupedal control and physical sand tests, or validates biped sinkage and slip on sand.Source: C. Granular Contact and Prediction… · p. 2
  • Granular resistance’s gravity scaling is unsettled, so the authors assess whether policy comparisons keep their sign across soil models rather than choosing a correct model.Reported evidence ranges from gravity-proportional drag to gravity-independent impact penetration, while lunar-simulant cone resistance falls only 9–29% at 1/6 g.Source: C. Granular Contact and Prediction… · p. 2
  • The study tests every policy at both gravities on rigid ground and 3D RFT soil, and at its training gravity on three held-out soil models.SONIC is included as a frozen reference on rigid ground.Source: Figure 2 · p. 3

III. METHOD

  • The 12 trained policies share one recipe and vary in gravity, geometry, ground, and initialization; SONIC is a frozen external reference.Soil ranges and reward settings also vary with gravity.Source: §III · p. 3

A. Training Setup

The training setup applies a shared PPO-based recipe to a Unitree G1 while varying rigid or granular contact and, for lunar soil, a stiffness range calibrated to walking foot sinkage. Gravity-randomized policies use the combined Earth and lunar soil ranges.

A. Training Setup

  • The G1 policies use GM-Loco reward terms reimplemented with PPO in Isaac Lab 3.0 on Newton with MuJoCo Warp.The model has 29 degrees of freedom; the actor observes ten frames of proprioception and previous actions with the velocity command, then outputs joint PD targets at 50 Hz.Source: A. Training Setup · p. 3
  • Commands span −0.5 to 1.0 m s−1 forward, ±0.3 m s−1 laterally, and ±1.0 rad s−1 yaw, with 20% zero-command episodes.Commands are resampled every 10 seconds in 20-second episodes, without a command curriculum.Source: A. Training Setup · p. 3
  • RFT-trained policies add per-foot 3D RFT forces summed over a 5 by 5 grid of sole elements, with rocks treated as rigid.The implementation matches published coefficients and original-code per-element forces, verifying the code but not lunar material behavior.Source: A. Training Setup · p. 3
  • Lunar training fixes internal friction at 0.9 and varies equivalent stiffness from 150 to 8000 kg m−3, calibrated by matching walking foot sinkage to Apollo bootprint stiffness scaled to G1 foot pressure.Earth training varies friction and effective density; gravity-randomized policies use the union of Earth and lunar ranges at every gravity.Source: A. Training Setup · p. 3

B. Policies and Training Budgets

The study varies gravity, terrain, and ground contact across G1 policies, with fine-tuning and gravity randomization as additional strategies. It also evaluates a frozen SONIC reference and adjusts selected design settings for gravity.

B. Policies and Training Budgets

  • Eight from-scratch policies cover every combination of Earth or Moon gravity, flat or rough terrain, and rigid or 3D RFT ground.Two Earth-to-Moon fine-tunes and two gravity-randomized policies complete the 12-policy set.Source: B. Policies and Training Budgets · p. 3
  • Gravity-randomized policies train from scratch with gravity drawn per episode, log-uniformly from 1.62 to 9.81 m s−2.The observation provides gravity direction but not magnitude, which policies can infer only from history.Source: B. Policies and Training Budgets · p. 4
  • Fine-tunes use 1.5×10^9 total environment steps, versus about 9.8×10^8 for a from-scratch run, with no Earth-to-Earth continuation control.Their Earth results describe continuations without Earth episodes and do not establish an inherent cost of lunar adaptation.Source: B. Policies and Training Budgets · p. 4

C. SONIC Baseline

  • The frozen SONIC checkpoint is tested on rigid ground only, using eight command profiles mapped to its planner inputs.Its planner receives no gravity or terrain input, so its references remain Earth-timed and level.Source: C. SONIC Baseline · p. 4

D. Gravity-Dependent Design

  • The gait has no clock: cadence and stride length emerge from training, while an air-time reward pays swing time beyond 0.5 s.The Froude number is v^2/(gL), with L = 0.78 m; at 1.0 m s−1 it is 0.79 on the Moon and 0.13 on Earth.Source: D. Gravity-Dependent Design · p. 4
  • At lunar gravity, energy and torque weights remain equal to Earth values, while only contact-force thresholds change with gravity.Lunar training also multiplies the landing-impact penalty by 9.81/1.62.Source: D. Gravity-Dependent Design · p. 4

IV. EXPERIMENTAL SETUP

The experimental setup uses generated lunar-like terrain and slopes, then evaluates policies across training and held-out soil models. The soil models differ in their contact assumptions and in how soil strength depends on gravity.

A. Terrain and Slopes

  • Terrain tiles are 8 m across at 0.1 m per pixel, with meter-scale craters, modeled rocks, and highland-like undulations.Evaluation uses 32 held-out tiles per family from disjoint generator seeds; rocks under 0.2 m are omitted, and rock statistics are extrapolated below measured sizes.Source: A. Terrain and Slopes · p. 4
  • Slope tests tilt gravity over flat rigid ground from 5° to 30°; only 30° exceeds the 26° training range.SONIC and four rigid-trained policies also traverse a 10° inclined mesh with vertical gravity.Source: A. Terrain and Slopes · p. 4

B. Soil Models

  • Tests use rigid ground, 3D RFT, and three held-out engines: MPM, SCM, and CRM.3D RFT covers every policy and geometry; MPM and CRM run only forward profiles 2 and 3, while 3D RFT and SCM run all eight profiles.Source: B. Soil Models · p. 4
  • MPM and CRM use lunar regolith parameters for 0–15 cm depth, while SCM uses a separate lunar Bekker fit.MPM bed stiffness is not calibrated to the bootprint modulus used to set 3D RFT soils; MPM also includes cohesion and footprint history absent from 3D RFT.Source: B. Soil Models · p. 4
  • Lunar 3D RFT soils are calibrated so Moon-Flat-RFT foot sinkage matches Apollo bootprints, making lunar soil results conditional on calibrated stiffness.Held-out engines use nominal lunar regolith at both gravities; its density is outside the Earth training range, and the compacted soil is twice as stiff as the stiffest lunar training soil.Source: B. Soil Models · p. 4
  • Soil strength scales differently with gravity across models: linearly in 3D RFT, through overburden but not linearly in MPM and CRM, and not at all in SCM.Held-out lunar-soil effects are claimed only where their sign agrees in both MPM and SCM; Earth-sand results and lunar-soil survival at Earth gravity come from 3D RFT alone.Source: B. Soil Models · p. 5

C. Evaluation Protocol and Metrics

Policies are tested across shared commands, environments, and seeds, with survival and locomotion metrics computed from episode outcomes. Statistical comparisons use per-cell, per-seed intervals and require consistent signs across seeds.

C. Evaluation Protocol and Metrics

  • Each 10 s episode starts with 2 s standing and then runs an 8 s command profile; failure occurs if the pelvis drops below 0.2 m or the base tilts beyond 0.8 rad.Tests remove pushes and training randomization, fix foot friction at 0.5, and share tiles, starts, commands, and seeds across policies.Source: C. Evaluation Protocol and Metrics · p. 5
  • Rigid and 3D RFT cells use 256 episodes per seed, while SCM uses 32 and MPM or CRM use six per policy and cell.MPM and CRM use one episode per seed for each of two forward profiles; some MPM episodes leaving the bed are excluded with their rigid-ground pairs.Source: C. Evaluation Protocol and Metrics · p. 5
  • Survival is the fraction of episodes reaching the end without failure, and signed progress integrates commanded-direction planar velocity until a fall or the motion phase ends.Projecting velocity onto the first commanded translational direction means heading drift does not count as progress.Source: C. Evaluation Protocol and Metrics · p. 5
  • The soil progress ratio compares mean signed progress on soil with the same engine’s rigid run on matching geometry and starts; values above 1 indicate more progress on soil.Survival is reported alongside it; tracking error averages forward and lateral velocity errors over the specified final constant-command window.Source: C. Evaluation Protocol and Metrics · p. 5
  • A finding requires the same difference sign in all three seeds, with each seed’s interval excluding zero.Survival differences use Newcombe intervals built from Wilson intervals; the method ignores shared tiles and starts and is therefore conservative.Source: C. Evaluation Protocol and Metrics · p. 5

V. RESULTS

The results examine gravity transfer, beginning with gait and survival on rigid ground. Transfer is asymmetric, while rough-trained gravity-randomized policies maintain high survival across key test cells at both gravities.

A. Gravity Transfer

  • Earth-trained policies survive 0.64 to 0.75 of flat rigid episodes at the Moon, while Moon-trained and fine-tuned policies fail every episode at Earth.SONIC survives at most 0.10 at the Moon on every rigid test cell; Earth+Moon-Rough-RFT reaches seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on key cells up to 20°.Source: A. Gravity Transfer · pp. 5, 7, Table II · p. 6
  • At 1 m s−1, the Earth-trained policy at Earth is airborne 0% of the time, while the Moon-trained policy at the Moon is airborne 49%.Across policies, Earth-trained gaits have duty factors around 0.6–0.9; Moon-trained and fine-tuned gaits at the Moon reach about 0.2–0.4.Source: A. Gravity Transfer · p. 5, Figure 3 · p. 6
  • Seed-mean survival is at least 0.84 at Earth and at least 0.96 at the Moon on every test cell of Table II up to 20°, with lowest seeds of 0.74 and 0.91, respectively.Source: A. Gravity Transfer · p. 7

B. Terrain and Slopes

Rough-terrain training improves tile and slope performance at training gravity, but its gains do not reliably transfer across gravity. Flat-trained policies are especially vulnerable to undulations, while SONIC performs well on Earth tiles but poorly at lunar gravity.

B. Terrain and Slopes

  • Combined-tile survival rises from 0.53 to 0.98 at Earth and from 0.80 to 0.99 at the Moon with rough-terrain training.The gain does not carry across gravity: Moon-trained policies fall on every tile family at Earth, and Earth-trained rough policies lose survival on every tile family at the Moon.Source: B. Terrain and Slopes · p. 7
  • On Earth tiles, flat-trained policies perform nearly as well as rough-trained ones on flat, crater, and rock tiles, but about half as well on undulations and combined tiles.Undulations are the costly feature for flat-trained policies at both gravities; craters and rocks cost little.Source: B. Terrain and Slopes · p. 7
  • At the Moon, the difference between rough- and flat-trained Earth policies on the 20° uphill grade is not consistent across seeds.At 30°, beyond the training range, most policies fail at both gravities; the best result is Earth→Moon-Rough-RFT downhill at the Moon.Source: B. Terrain and Slopes · p. 7
  • At Earth, SONIC has a survival of 1.00 on flat, crater, and rock tiles and the inclined mesh, and 0.90 to 0.91 on undulations and combined tiles.Source: B. Terrain and Slopes · p. 7
  • At Earth, rough-trained policies survive the 20° grade more often than flat-trained policies in every direction and pair except Earth-Rough-Rigid downhill.In that exception, one seed falls in most episodes; at 26°, policies fail, while at the Moon flat-trained policies approach zero uphill survival by 26° and lunar rough-trained policies decline more gradually.Source: B. Terrain and Slopes · p. 7
  • Survival on the 10° inclined mesh is close to that on the same-grade tilted-gravity slope in all but three cells.SONIC is tested on slopes only on the inclined mesh, where gravity remains vertical.Source: B. Terrain and Slopes · p. 7

C. Soil Training

Soil training improves some Earth-gravity outcomes on sand, but its effects are less consistent on the stiffer lunar soil. Moon-trained policies retain most of their soil-episode performance in the reported tests.

C. Soil Training

  • On flat sand, Earth-Rough-RFT survives 0.99 of episodes versus 0.33 for Earth-Rough-Rigid.Both RFT-trained Earth policies also survive combined tiles under sand more often than their rigid-trained neighbors.Source: C. Soil Training · p. 7
  • On the stiffer lunar soil at Earth gravity, only the flat-trained pair retains a survival gain on tiles, while the rough pair shows no consistent difference.All four Earth-trained policies survive nearly every flat episode on this soil.Source: C. Soil Training · p. 7
  • On lunar soil at the Moon, Moon-Flat-RFT and Moon-Rough-RFT differ from rigid-trained neighbors by at most a few hundredths in survival on every soil cell.The high 3D RFT survival on combined tiles mainly reflects falls on the rigid reference.Source: C. Soil Training · pp. 7–8
  • Across four calibrated lunar soils, Moon-trained and fine-tuned policies retain at least 0.93 of tile episodes and nearly all flat episodes.The tested soils range from loose regolith to compacted soil twice as stiff as any lunar training soil.Source: C. Soil Training · p. 8

D. Training Strategies for the Moon

Lunar adaptation can preserve Moon performance while differing sharply in whether policies retain Earth walking. Soil-model tests find little loss of Moon-trained progress on lunar soils in sampled rollouts, with claims bounded by the tested engines and low G1 foot pressure.

D. Training Strategies for the Moon

  • Moon-Flat-Rigid, Earth→Moon-Flat-Rigid, and Earth+Moon-Flat-Rigid survive every flat rigid episode at the Moon with similar tracking error.Only Earth+Moon-Flat-Rigid retains most Earth survival; Moon-Flat-Rigid and Earth→Moon-Flat-Rigid walk in no Earth episode. Fine-tuning adds 5k iterations, about 0.49×10^9 steps, when an Earth-trained policy already exists.Source: D. Training Strategies for the Moon · p. 8
  • On rigid combined tiles at the Moon, the three rough RFT strategies are within a few hundredths in survival, but only Earth+Moon-Rough-RFT keeps walking at Earth.The three strategies show no large loss in MPM.Source: D. Training Strategies for the Moon · p. 8

E. Dependence on the Soil Model

  • The authors claim held-out lunar-soil effects only when MPM and SCM agree in sign and the difference holds in all three seeds.3D RFT agreement with MPM alone is not treated as robust to gravity scaling because both resistance models rise with gravity; CRM checks flat beds only.Source: E. Dependence on the Soil Model · p. 8
  • In sampled rollouts, Moon-trained policies retain most rigid-ground progress on lunar soil, with per-seed ρv of 0.84 to 1.39 except one seed with a short rigid reference.The scope is the G1's low foot pressure; the authors expect, without isolating it, that this explains why lunar soil behaved close to rigid in all engines.Source: E. Dependence on the Soil Model · p. 8
  • At lunar gravity, 3D RFT makes walking easier than rigid ground for most policies, while the cause is not isolated.A proposed explanation is that resistive force opposes foot motion and damps destabilizing rebounds; soil claims therefore rest on held-out engines.Source: E. Dependence on the Soil Model · pp. 8–9
  • Soil-training effects on progress at Earth gravity on lunar soil are not robust across seeds and engines: no difference keeps a common sign in all three seeds of both MPM and SCM.MPM and SCM agree on the sign for the flat pair but disagree for the rough pair; single falls in six MPM episodes set the means.Source: E. Dependence on the Soil Model · p. 9

VI. DISCUSSION AND CONCLUSION

The discussion reports asymmetric gravity transfer, selective benefits from rough and soil training, and recommends gravity randomization among the tested strategies. Lunar soil conclusions remain conditional on the contact models and soil stiffness.

VI. DISCUSSION AND CONCLUSION

  • Earth-trained policies retain only part of their survival at the Moon, Moon-trained and fine-tuned policies cannot stand at Earth, and SONIC fails at the Moon.The transfer asymmetry can occur even on flat rigid ground.Source: §VI · p. 9
  • Rough training raises combined-tile survival at both gravities, while soil-training benefits depend on the terrain, gravity, and policy.On the stiffer lunar soil, soil training helps only flat-trained Earth policies at Earth and changes Moon-trained survival at the Moon by at most a few hundredths.Source: §VI · p. 9
  • The rough-3D-RFT gravity-randomized policy reaches seed-mean survival of at least 0.84 at Earth and 0.96 at the Moon on every key cell up to 20°; the authors recommend it.Moon fine-tuning adds half a from-scratch run but removes Earth walking in continuations without Earth episodes; gravity randomization costs one from-scratch run.Source: §VI · p. 9
  • Terrain statistics extrapolate below measured sizes, omit rocks under 0.2 m, and combine lunar soil parameters across sites, depths, and test methods.Training and tests use no observation noise, and CRM is tested only on flat beds.Source: §VI · p. 9
  • Lunar-soil results hold only where MPM and SCM agree, because the models scale soil resistance differently and cone resistance falls far less than linearly.The soil results apply at the G1’s low lunar foot pressure, about 3.9 kPa over the full sole; the authors did not isolate why lunar soil behaved close to rigid.Source: §VI · p. 9
  • All findings are simulation predictions for one robot, with no test applying lunar gravity to a robot and soil together; SONIC is one checkpoint, not a controller family.The paper identifies a ground test of soil resistance at reduced gravity under a foot-sized load as the measurement that would most reduce soil uncertainty.Source: §VI · p. 9
  • Survival alone may be too strict at the Moon; a fall-tolerant objective could score safe falls, recovery, and time to resume walking.The discussion notes repeated Apollo surface falls and proposes measuring recovery rate and time to resume walking.Source: §VI · p. 9

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