cs.ROOct 25, 2026

HumanoidNDM: Closing the Training-Deployment Gap of Motion Tracking via Humanoid Neural Dynamics Model

Authors: Chao Chen, Zhenrong Wang, Jilong Wang, Yusen Feng, Jiangran Lyu, Li Yi, He Wang

Organizations: CFCS, School of Computer Science, Peking University · Galbot · Institute of Automation, Chinese Academy of Sciences · Beijing Academy of Artificial Intelligence · 

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Abstract

Humanoid robots have recently achieved remarkable success in motion tracking. However, during real-world deployment, robots inevitably encounter dynamics gaps arising from either extra physical disturbances or inaccurate simulation modeling, resulting in a significant training-deployment gap. Therefore, effectively leveraging real-world data to fine-tune policies represents the crucial last mile for robust deployment. To bridge this gap, we propose HumanoidNDM, an online fine-tuning framework for humanoid motion tracking driven by a real-world-trained neural dynamics model. First, in the data collection stage, we introduce a low-frequency reference perturbation method with an adaptive intensity mechanism, balancing deployment feasibility and exploration efficiency. Second, for the model training stage, we train a robust history-based, proprioceptive neural dynamics model in Euclidean space by incorporating differentiable forward kinematics, eliminating the reliance on costly motion capture systems. Finally, in the policy fine-tuning stage, we directly fine-tune the policy via backpropagated model gradients, achieving high data efficiency. Through physical validation on the Unitree G1 robot, we demonstrate that HumanoidNDM enables rapid real-world adaptation to various perturbations, representing the first online, MoCap-free fine-tuning framework for humanoid tracking policies.

Figures & tables

Figure 1: Comparison of direct transfer (left two frames) and fine-tuned performance (right two frames): (a) Swallow Balance : 1.5 kg weights on each calf; (b) Arm Swing : 1.5 kg weight on the left hand; (c) Pen Capping : 0.75 kg load on the left hand; (d) Lateral Raise : two elastic bands attached to wrists; (e) Bowing : damaged arm motor; and (f) Walking : 2 kg water bucket in hand.
MethodDeployment FeasibilityPolicy-Relevant CoverageAdaptive Intensity
Uncorrelated Action Noise [ 4 , 48 ]×\times✓\checkmark×\times
Observation Perturbation [ 23 , 29 ]×\times×\times×\times
Passive Dynamic Exploration [ 18 , 15 ]✓\checkmark×\times×\times
Temporally Correlated Noise [ 31 , 7 ]∼\sim✓\checkmark×\times
Ours (FENCE)✓✓✓
Table 1: Comparison of exploration strategies. “ ∼\sim ” denotes partial or conditional capability.
Figure 2: Pipeline of HumanoidNDM. Left: HumanoidNDM uses a simulation-trained policy to collect real-world data for online fine-tuning. Each iteration comprises three stages: Data Collection , Model Training , and Policy Fine-tuning . Right: The key components of each stage.
DisturbanceExtra WeightScaled KPSmall Friction
TrajectoryMethodElink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}Elink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}Elink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}
WalkPPO w/ Disturb.3.110.282.013.832.740.281.701.942.450.241.461.70
Direct Transfer5.33 ±\pm 0.000.55 ±\pm 0.003.29 ±\pm 0.003.81 ±\pm 0.004.92 ±\pm 0.000.56 ±\pm 0.003.20 ±\pm 0.003.80 ±\pm 0.004.64 ±\pm 0.000.49 ±\pm 0.003.06 ±\pm 0.003.84 ±\pm 0.00
ASAP4.09 ±\pm 0.200.41 ±\pm 0.033.30 ±\pm 0.092.93 ±\pm 0.202.83 ±\pm 0.120.47 ±\pm 0.022.67 ±\pm 0.052.02 ±\pm 0.152.49 ±\pm 0.080.31 ±\pm 0.012.81 ±\pm 0.012.35 ±\pm 0.09
RWM4.71 ±\pm 0.150.40 ±\pm 0.033.15 ±\pm 0.072.91 ±\pm 0.114.71 ±\pm 0.280.32 ±\pm 0.032.55 ±\pm 0.072.98 ±\pm 0.384.37 ±\pm 0.640.36 ±\pm 0.142.11 ±\pm 0.182.33 ±\pm 0.19
HumanoidNDM3.59 ±\pm 0.240.27 ±\pm 0.032.15 ±\pm 0.072.56 ±\pm 0.232.90 ±\pm 0.130.22 ±\pm 0.021.80 ±\pm 0.041.86 ±\pm 0.132.49 ±\pm 0.090.13 ±\pm 0.011.54 ±\pm 0.011.55 ±\pm 0.08
Table 2: Comparison of HumanoidNDM and baselines across 5 random trials (mean ±\pm std).
Figure 3: Comparison between exploration methods.
MethodPolicy Evaluation PerformanceData Collection Performance
Elink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowSqposS_{\text{qpos}} (×10−3)(\times 10^{-3}) ↓\downarrowSroll-pitchS_{\text{roll-pitch}} (×10−4)(\times 10^{-4}) ↓\downarrow
ASAP3.68 ±\pm 0.203.03 ±\pm 0.104.79 ±\pm 6.470.95 ±\pm 3.06
ASAP w/ FENCE3.53 ±\pm 0.183.13 ±\pm 0.085.84 ±\pm 6.271.23 ±\pm 4.25
RWM4.42 ±\pm 0.232.68 ±\pm 0.1127.44 ±\pm 13.8211.06 ±\pm 9.73
RWM w/ FENCE4.23 ±\pm 0.352.72 ±\pm 0.135.43 ±\pm 5.121.48 ±\pm 4.19
Table 3: Effectiveness of FENCE on baselines (mean ±\pm std).
Figure 4: Left: Training w/ and w/o Euclidean-space objective. Right: Model w/ and w/o history.
SettingSwallow Balance (w/ leg weights)Arm Swing (w/ hand weights)Pen Capping (w/ hand weight)
MethodElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowair time (s) ↑\uparrowElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowarm height (m) ↑\uparrowElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowEE distance (cm) ↓\downarrow
PPO w/ Disturb.4.72 ±\pm 0.282.90 ±\pm 0.390.40 ±\pm 0.112.72 ±\pm 0.012.34 ±\pm 0.031.43 ±\pm 0.026.58 ±\pm 0.003.27 ±\pm 0.000.00 ±\pm 0.00
Direct Transfer5.34 ±\pm 0.063.40 ±\pm 0.070.00 ±\pm 0.005.85 ±\pm 0.023.33 ±\pm 0.010.98 ±\pm 0.006.96 ±\pm 0.003.50 ±\pm 0.003.50 ±\pm 0.00
HumanoidNDM4.44 ±\pm 0.132.98 ±\pm 0.341.90 ±\pm 0.612.98 ±\pm 0.002.30 ±\pm 0.011.40 ±\pm 0.016.82 ±\pm 0.003.36 ±\pm 0.000.00 ±\pm 0.00
SettingLateral Raise (w/ elastic bands)Walking (w/ water bucket)Bowing (w/ damaged motor)
MethodElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowarm height (m) ↑\uparrowElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrowdeviation angle ( ∘ ) ↓\downarrowElink_pos↓E_{\text{link\_pos}}\downarrowEqpos↓E_{\text{qpos}}\downarrownoise level (dB) ↓\downarrow
Table 4: Performance under added weight disturbances (top) and hard-to-model disturbances (bottom) (mean ±\pm std). The third column represents the task-specific metric reflecting task completeness.
MethodSqpos↓\boldsymbol{S_{\text{qpos}}\downarrow}Sroll-pitch↓\boldsymbol{S_{\text{roll-pitch}}\downarrow}
FENCE0.099 ±\pm 0.0180.126 ±\pm 0.023
Action Gaussian Noise1.275 ±\pm 0.3131.678 ±\pm 0.455
Action OU Noise0.707 ±\pm 0.1800.739 ±\pm 0.210
Obs Gaussian Noise1.151 ±\pm 0.3151.033 ±\pm 0.218
No Noise0.076 ±\pm 0.0050.106 ±\pm 0.008
Table 5: Real-world comparison of exploration methods (mean ±\pm std).
Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

VariableValue
Data Collection
Max perturbation frequency ( kck_{c} )1.0 Hz
Roll-pitch termination threshold1.0
Radial bin number2
Directional bin number16
MAB exploration scale ( β\beta )0.05
Appendix
Table 6: Hyperparameters of HumanoidNDM
Figure 5: Walk: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 6: Balance: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 7: Squat: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 8: Swing: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 9: Stride: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 10: Comparison between the adaptive and fixed σ\sigma under the default simulation setting.
Figure 11: Comparison between adaptive and fixed perturbation intensities in real-world experiments on swing and stride motions.
Figure 12: Comparison between the adaptive and fixed σ\sigma using policies with varying degrees of responsiveness ( top : weak ; middle : medium ; bottom : strong ).
DisturbanceExtra WeightScaled KPSmall Friction
TrajectoryMethodElink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}Elink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}Elink_posE_{\text{link\_pos}}Elink_rotE_{\text{link\_rot}}EqposE_{\text{qpos}}Ekey_qposE_{\text{key\_qpos}}
JumpPPO w/ Disturb.3.030.341.901.644.150.502.863.634.420.312.051.77
Direct Transfer6.74 ±\pm 0.001.56 ±\pm 0.004.77 ±\pm 0.006.50 ±\pm 0.007.41 ±\pm 0.001.77 ±\pm 0.005.01 ±\pm 0.008.75 ±\pm 0.007.53 ±\pm 0.001.80 ±\pm 0.004.92 ±\pm 0.006.74 ±\pm 0.00
ASAP3.18 ±\pm 0.110.63 ±\pm 0.073.30 ±\pm 0.143.15 ±\pm 0.207.08 ±\pm 0.091.98 ±\pm 0.124.56 ±\pm 0.165.98 ±\pm 0.414.59 ±\pm 0.090.47 ±\pm 0.033.52 ±\pm 0.025.05 ±\pm 0.27
RWM5.79 ±\pm 0.990.92 ±\pm 0.333.49 ±\pm 0.043.29 ±\pm 0.335.66 ±\pm 0.030.75 ±\pm 0.023.99 ±\pm 0.015.81 ±\pm 0.254.73 ±\pm 0.040.64 ±\pm 0.013.73 ±\pm 0.033.60 ±\pm 0.03
HumanoidNDM3.31 ±\pm 0.120.37 ±\pm 0.012.97 ±\pm 0.032.42 ±\pm 0.094.68 ±\pm 0.220.55 ±\pm 0.033.25 ±\pm 0.055.78 ±\pm 0.344.28 ±\pm 0.980.46 ±\pm 0.192.63 ±\pm 0.282.40 ±\pm 0.68
Appendix
Table 7: Performance comparison of HumanoidNDM and baseline methods on the jump motion across 5 random trials.
Figure 13: Jump: Extra Weight (top), Scaled KP (middle), Small Friction (bottom).
Figure 14: Comparison of HumanoidNDM with and without pretrained NDM.
Figure 15: Model visualization and performance for balance motion with extra weight.
Figure 16: Model visualization and performance for squat motion with extra weight.
Figure 17: Model visualization and performance for walk motion with scaled KP.
Figure 18: Model visualization and performance for stride motion with small friction.
Figure 19: Model visualization and performance for swing motion with small friction.
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