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

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

cs.ROOct 21, 2026

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

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

Organizations: Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305, USA

Abstract

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.

Figures & tables

Fig. 1: A G1 walking on simulated lunar regolith. An Earth-to-Moon fine-tuned policy walks at $1\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}$ on an MPM regolith bed at lunar gravity. The insets show an Earth-trained policy falling at lunar gravity and a footprint left in the bed.

Fig. 2: Study design. Policies train in Isaac Lab on Newton with MuJoCo Warp over gravity, geometry, and ground. Each frozen, blind G1 policy maps proprioception and the velocity command to joint targets. Tests run every policy at both gravities on rigid ground and on 3D RFT soil, and at its training gravity on three soil models held out of training. SONIC enters as a frozen reference on rigid ground.

Name	$g$ [m/s 2 ]	Geometry	Ground	Init.
Earth-Flat-Rigid	9.81	Flat	Rigid	Scratch
Earth-Flat-RFT	9.81	Flat	RFT	Scratch
Earth-Rough-Rigid	9.81	Rough	Rigid	Scratch
Earth-Rough-RFT	9.81	Rough	RFT	Scratch
Moon-Flat-Rigid	1.62	Flat	Rigid	Scratch
Moon-Flat-RFT	1.62	Flat	RFT	Scratch

TABLE I: Policies trained in this study

	Flat		Combined tiles		Slope $20\text{\,}\mathrm{\SIUnitSymbolDegree}$		Slope $30\text{\,}\mathrm{\SIUnitSymbolDegree}$
Policy	Rigid	Soil	Rigid	Soil	Up	Down	Up	Down
At Earth
Earth-Flat-Rigid	1.00	0.96 [0.92,0.99]	0.53 [0.50,0.56]	0.27 [0.22,0.34]	0.36 [0.27,0.44]	0.19 [0.08,0.37]	0.00	0.00
Earth-Flat-RFT	1.00 [0.99,1.00]	1.00	0.70 [0.62,0.76]	0.69 [0.61,0.76]	0.08 [0.00,0.21]	0.26 [0.21,0.33]	0.00	0.00
Earth-Rough-Rigid	1.00	0.33 [0.11,0.54]	0.98 [0.98,0.99]	0.30 [0.20,0.43]	1.00	0.68 [0.05,0.99]	0.00	0.00
Earth-Rough-RFT	1.00	0.99 [0.98,1.00]	0.98 [0.97,0.98]	0.87 [0.72,0.95]	0.99 [0.97,1.00]	0.98 [0.93,1.00]	0.00	0.00

TABLE II: Survival on the key test cells at both gravities

Fig. 3: Gait timing against Froude number. (a, b) Foot contact timelines walking at

1\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

for an Earth-trained policy at Earth, airborne 0% of the time, and a Moon-trained policy at the Moon, airborne 49% of the time. (c–e) Speed over command, duty factor, and flight fraction against the Froude number

v^{2}/(gL)

for each policy group of the legend and SONIC. Hollow markers are tested at Earth and filled markers at the Moon. Each marker is the mean over the policies and seeds of one group at one command speed of 0.25, 0.5, or

1.0\text{\,}\mathrm{m}\text{\,}{\mathrm{s}}^{-1}

on flat rigid ground, 12 policy seeds for the Earth- and Moon-trained groups, 6 for the fine-tuned and gravity-randomized groups, and the single SONIC checkpoint. Each policy seed contributes the mean over its surviving episodes, and the bars span the lowest to the highest policy seed. Policy seeds with fewer than 25% surviving episodes are left out, which removes SONIC at the Moon and the Moon-trained and fine-tuned policies at Earth.

		Tiles, $S\uparrow$					Mesh, $S\uparrow$		Comb.
Policy	Test	Flat	Crat.	Rock	Und.	Comb.	Up	Down	$e_{v}\downarrow$
Earth-Flat-Rigid	Earth	1.00	0.98	0.98	0.57	0.53	0.74	1.00	0.10
Earth-Flat-Rigid	Moon	0.64	0.66	0.68	0.45	0.45	0.64	0.39	0.25
Earth-Rough-Rigid	Earth	1.00	1.00	1.00	0.99	0.98	1.00	1.00	0.04
Earth-Rough-Rigid	Moon	0.74	0.74	0.76	0.47	0.43	0.75	0.62	0.26
Moon-Flat-Rigid	Earth	0.00	0.00	0.00	0.00	0.00	0.00	0.00	–

TABLE III: Survival and tracking on held-out terrain at both gravities

Fig. 4: Slope envelope at both gravities. Survival against grade, uphill and downhill, with gravity tilted over a borderless rigid plane. Rough-trained policies are solid and flat-trained policies dashed, for each policy group of the legend, averaged over its rigid- and RFT-trained policies where both exist and over three seeds. Seed ranges at 20 and

30\text{\,}\mathrm{\SIUnitSymbolDegree}

are in Table II , and the supplement lists survival per seed at every grade, and its seed sign-rule table tests each slope claim per seed. The shaded range lies beyond the training slopes.

	3D RFT		MPM		SCM		CRM
Policy	Flat	Comb.	Flat	Comb.	Flat	Comb.	Flat
Earth-Flat-Rigid	1.04	0.80	0.76	1.26	0.96	1.37	0.98
Earth-Flat-RFT	1.07	0.91	0.86	1.24	1.05	1.18	1.07
Earth-Rough-Rigid	1.05	0.93	1.03	1.04	1.06	0.91	1.03
Earth-Rough-RFT	0.94	0.93	1.06	1.02	1.03	0.95	1.07
Moon-Flat-Rigid	1.04	1.35	1.00	1.05	1.04	1.01	1.09

TABLE IV: Performance of the grid policies on soil in each engine

	Moon				Earth		Total
Policy	$S\uparrow$	$e_{v}\downarrow$	$\rho_{v}^{\rm RFT}$	$\rho_{v}^{\rm MPM}$	$S\uparrow$	$e_{v}\downarrow$	Iter.	Steps
Moon-Flat-Rigid	1.00	0.03	–	–	0.00	–	10	0.98
Earth $\to$ Moon-Flat-Rigid	1.00	0.03	–	–	0.00	–	15	1.47
Earth+Moon-Flat-Rigid	1.00	0.02	–	–	0.92	0.02	10	0.98
Earth-Flat-Rigid	0.64	0.16	–	–	1.00	0.01	10	0.98
Moon-Rough-RFT	0.97	0.10	1.08	1.03	0.00	–	10	0.98

TABLE V: Comparison of training strategies for the Moon

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Jun 9, 2026J/K move · Enter open · S save

Locomotion analysis of a quadruped interacting with the lunar granular surface

Yash J Vyas

Department of Industrial Engineering, University of Padua

Granular Terrain Locomotion Robotics Simulation Gait Analysis Robotics Terrain-Aware Robot Locomotion Robot Locomotion+2

Open paper AskPDF arXiv

Deploying legged robots in extra-terrestrial environments includes many challenges due to complex terrain interactions, energy, and thermal constraints. For effective mechanical design of a lunar exploration quadrupedal robot, careful consideration of motor torques, energy expenditure, and cost of transport is required. The lunar surface is composed of granular regolith, which impacts the locomotion of legged robots and their performance. Locomotion algorithms trained with rigid contact assumptions are also ineffective when applied to environments with soft contacts, such as granular surfaces, which can result in instability and poor tracking. In this report, the physical modelling of the granular lunar surface-robot foot contacts is applied to a simulation environment with locomotion trained using Reinforcement Learning. A comparison is conducted between the policy trained on rigid contact and soft contact environments, analysing the gait and locomotion performance metrics. The analysis demonstrates that soft contacts simulating regolith surfaces pose additional challenges for Reinforcement Learning based training, result in a qualitatively different gait, and increase the overall energy expenditure.

Abstract

Humanoid Robot Locomotion

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