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 1ms−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\SIUnitSymbolDegree
Slope 30\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 1ms−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 v2/(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 1.0ms−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↑
Mesh, S↑
Comb.
Policy
Test
Flat
Crat.
Rock
Und.
Comb.
Up
Down
ev↓
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\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↑
ev↓
ρvRFT
ρvMPM
S↑
ev↓
Iter.
Steps
Moon-Flat-Rigid
1.00
0.03
–
–
0.00
–
10
0.98
Earth → 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
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.
Yash J Vyas
Department of Industrial Engineering, University of Padua
Robotic systems for lunar surface operations must act autonomously and preserve their own integrity in an environment where failures are unrecoverable and continuous supervision is impossible. This paper presents a Constrained Reinforcement Learning framework for quadrupedal mobile manipulators that learns a single whole-body policy for tracking a 6D end-effector pose specified in task space, with operational limits enforced during learning through a constrained learning mechanism. We introduce a reward formulation in which the transition between locomotion and manipulation emerges from the reward geometry rather than from an explicit gating mechanism, a stability term derived from the Gravito-Inertial Inclination Margin and motivated by the reduced-gravity dynamics of the lunar surface, and a design rule for reward regularization that follows from the multiplicative structure of the termination-based objective. The framework is evaluated in a lunar-analog simulation spanning three terrain morphologies at five difficulty levels under lunar gravity, with regolith contact properties calibrated to the JSC-1a simulant and varied from loose to dense. The learned policy attains mean position and orientation errors of 3.22 cm and 6.83 deg. under nominal conditions, retains this precision across regolith densities and over the operationally representative range of terrain difficulty, and reduces soft-constraint violation time by up to an order of magnitude relative to an unconstrained baseline while incurring no hard-constraint violations.
Alvaro Belmonte-Baeza, Miguel Cazorla, Gabriel J. García +2
Legged robots can extend planetary exploration to rugged and discontinuous terrain that is inaccessible to conventional rovers. In lunar gravity, jumping further expands this mobility by enabling robots to cross obstacles and gaps that cannot be traversed by walking alone. We present a multistage reinforcement-learning approach that produces a single end-to-end control policy for commanded point-to-point jumping under lunar gravity. The resulting policy has a simple architecture and relies exclusively on mission-compatible onboard sensing, making its deployment on a real lunar mission plausible. In simulation, the learned policy performs accurate point-to-point jumps with landing errors smaller than the robot's body size. We analyze the torque and power demands of lunar jumping and characterize performance degradation under extreme outlier events, including control-update freezes of up to \SI{1}{s} during flight. Hardware transfer demonstrates that the policy can successfully execute a vertical jump under lunar-gravity offloading. Furthermore, the measured torque and power profiles are consistent with the simulation results and remain within the robot's hardware limits.
Levin Müller, Oliver Fischer, Marco Trentini +2
ETH Zurich, Robotics Systems Lab; Leonhardstrasse 21, 8092 Zurich, Switzerland.