Achieving general-purpose humanoid control requires a delicate balance between the precise execution of commanded motions and the flexible, anthropomorphic adaptability needed to recover from unpredictable environmental perturbations. Current general controllers predominantly formulate motion control as a rigid reference-tracking problem. While effective in nominal conditions, these trackers often exhibit brittle, non-anthropomorphic failure modes under severe disturbances, lacking the generative adaptability inherent to human motor control. To overcome this limitation, we propose Heracles, a novel state-conditioned diffusion middleware that bridges precise motion tracking and generative synthesis. Rather than relying on rigid tracking paradigms or complex explicit mode-switching, Heracles operates as an intermediary layer between high-level reference motions and low-level physics trackers. By conditioning on the robot's real-time state, the diffusion model implicitly adapts its behavior: it approximates an identity map when the state closely aligns with the reference, preserving zero-shot tracking fidelity. Conversely, when encountering significant state deviations, it seamlessly transitions into a generative synthesizer to produce natural, anthropomorphic recovery trajectories. Our framework demonstrates that integrating generative priors into the control loop not only significantly enhances robustness against extreme perturbations but also elevates humanoid control from a rigid tracking paradigm to an open-ended, generative general-purpose architecture.
Figures & tables
Figure 1: Heracles synthesizes diverse, anthropomorphic recovery motions via state-conditioned diffusion. In contrast to recovery policies trained with termination tricks that converge to a limited set of stereotypical maneuvers, Heracles leverages its generative middleware to produce a rich repertoire of agile, human-like recovery behaviors, enabling more general and robust responses across a wide range of extreme perturbations.
Figure 2: Overview of the Heracles framework. (a) A flow matching model D^θ learns to synthesize feasible keyframe trajectories conditioned on the current state. (b) Reference motions are quantized into discrete tokens via FSQ, shared by reconstruction and action prediction heads. (c) At inference, the middleware generates trajectories through closed-loop replanning for the motion tracker to execute.
Table 1: Training configuration for the general-purpose physics tracker. Left: reward function with exponential tracking terms and regularization penalties. Right: domain randomization ranges for command-level, physical, and external disturbance parameters.
Tracker Hyperparameter
Value
Parallel environments
16,384
Rollout horizon
24 steps
Discount factor γ
0.99
GAE λ
0.95
PPO epochs / mini-batches
5 / 4
Clipping ratio ϵ
0.2
Table 2: Training hyperparameters for the physics tracker and the trajectory generator. Left: PPO-based tracker training configuration. Right: flow matching trajectory generator architecture, optimization, and inference settings.
Method
Component
Configuration
MLP
Actor
[4096,2048,1024,512,256] MLP
Critic
[4096,2048,1024,512,256] MLP
Transformer
Tokenizer
[512,512] MLP ×2 modalities → 3 tokens (512-dim)
Backbone
3-layer, 4-head, 512-dim Transformer
Action head
[2048,1024,256] MLP
Critic
[3072,1536,768,512] MLP
Table 3: Network architecture specifications for all evaluated methods. [⋅] denotes MLP hidden-layer widths. iFSQ ∗ covers all iFSQ variants (iFSQ BM , iFSQ +H , iFSQ), which share the same network but differ in observation design.
Method
Obs.
Tokenizer
Policy
Traj. Gen.
MLP
BM
–
MLP
✗
Transformer
BM
–
Trans.
✗
VQ-VAE
BM
VQ
Enc-Dec
✗
SONIC
SONIC
–
SONIC
✗
iFSQ BM
BM+H
iFSQ
Enc-Dec
✗
iFSQ +H
† +H
iFSQ
Enc-Dec
✗
Table 4: Component configuration and quantitative comparison of all evaluated methods. (a) Obs. column: BM = BeyondMimic-style Liao et al. (2025) ; † = proposed ( Sec. 3.3 ); +H = with height features. ✓/✗ indicates presence or absence of the trajectory generator. (b) Completion rate measures the fraction of reference frames for which the root height error remains below 0.3 m and the root orientation error stays below 1.2 rad; tracking errors are reported for joint positions, root height, root orientation (excl. yaw), and root linear velocity. Blue cells mark the best result per metric. Colored percentages show relative change from MLP: teal = better, red = worse.
Figure 3: Qualitative sim-to-sim comparison on an out-of-distribution martial arts sequence. Each row shows a different method tracking the same reference motion on a Unitree G1 humanoid alongside a reference ghost in MuJoCo. MLP, Transformer, and SONIC collapse early; VQ-VAE barely tracks the motion. Among our ablations, iFSQ BM and iFSQ survive without falling, while iFSQ +H falls but later recovers. Heracles (Ours) tracks the full sequence most accurately, demonstrating the strongest robustness to OOD motions.
Figure 4: Real-world motion tracking across diverse and dynamic behaviors. Real-world experiments demonstrate that our model generalizes to a broad spectrum of motions, from everyday locomotion (walk, run) to highly dynamic skills (kick, 360° kick) and human-object interaction.
Method
CR (%) ↑
Joint Err (rad) ↓
Height Err (m) ↓
Ori Err (rad) ↓
LinVel Err (m/s) ↓
MLP
44.0
2.1720
0.3586
1.0157
0.2710
Transformer
40.6 ( −7.7% )
2.8309 ( −30.3% )
0.3706 ( −3.3% )
0.8355 ( +17.7% )
0.2708 ( +0.1% )
VQ-VAE
69.8 ( +58.6% )
2.5700 ( −18.3% )
0.1898 ( +47.1% )
0.4307 ( +57.6% )
0.2719 ( −0.3% )
SONIC
42.8 ( −2.7% )
2.9897 ( −37.6% )
0.3342 ( +6.8% )
0.8629 ( +15.0% )
0.2895 ( −6.8% )
iFSQ BM
52.4 ( +19.1% )
2.4482 ( −12.7% )
0.2880 ( +19.7% )
0.9109 ( +10.3% )
0.3134 ( −15.6% )
iFSQ +H
52.7 ( +19.8% )
1.7660 ( +18.7% )
0.0419 ( +88.3% )
0.2744 ( +73.0% )
0.2793 ( −3.1% )
Table 5: Fall-and-recovery evaluation on challenging lie-to-stand, prone-to-stand, and stand-to-lie sequences. CR denotes completion rate. Blue marks the best result per metric. Colored percentages show relative change from MLP: teal = better, red = worse.
Variant
CR (%) ↑
Joint Err (rad) ↓
Height Err (m) ↓
Ori Err (rad) ↓
LinVel Err (m/s) ↓
Heracles (full)
90.6
1.3272
0.0764
0.2728
0.2325
w/o directional warm start
87.2 (-3.8%)
1.6236 (-22.3%)
0.0962 (-25.9%)
0.3393 (-24.4%)
0.2423 (-4.2%)
w/o noisy-state augmentation
78.6 (-13.2%)
1.8896 (-42.4%)
0.1463 (-91.5%)
0.4318 (-58.3%)
0.2182 (+6.1%)
w/o kinematics-aware weighting
82.1 (-9.4%)
1.6931 (-27.6%)
0.1200 (-57.1%)
0.4055 (-48.6%)
0.2394 (-3.0%)
Table 6: Ablation study on the trajectory generator’s key design components. All variants are evaluated on the full 101-sequence test set using the same iFSQ tracker. Blue marks the best result per metric. Colored percentages show relative change from Heracles (full): teal = better, red = worse.
Figure 5: Qualitative sim-to-sim comparison on an OOD lie-to-stand sequence. Same setup as Fig. 3 . MLP, Transformer, SONIC, and iFSQ BM fail to stand up; VQ-VAE, iFSQ +H , and iFSQ partially track the motion. Heracles (Ours) completes the full lie-to-stand transition and most accurately tracks the root position.
Figure 6: Emergent semantic clustering in the learned iFSQ codebook. Each point represents a quantized motion token projected into 3D via PCA; colors denote motion categories. Despite receiving no category labels during training, the codebook self-organizes into semantically coherent clusters corresponding to distinct motor skills.
Figure 7: Omnidirectional fall recovery motion tracking. Real-world experiments demonstrate that our model generalizes to arbitrary lie-to-stand recovery motions, successfully handling varied initial fallen configurations and recovery directions without task-specific engineering.
Physics-based humanoid control relies on training with motion datasets that have diverse data distributions. However, the fixed difficulty distribution of datasets limits the performance ceiling of the trained control policies. Additionally, the method of acquiring high-quality data through professional motion capture systems is constrained by costs, making it difficult to achieve large-scale scalability. To address these issues, we propose a closed-loop automated motion data generation and iterative framework. It can generate high-quality motion data with rich action semantics, including martial arts, dance, combat, sports, gymnastics, and more. Furthermore, our framework enables difficulty iteration of policies and data through physical metrics and objective evaluations, allowing the trained tracker to break through its original difficulty limits. On the PHC single-primitive tracker, using only approximately 1/10 of the AMASS dataset size, the average failure rate on the test set (2201 clips) is reduced by 45% compared to the baseline. Finally, we conduct comprehensive ablation and comparative experiments to highlight the rationality and advantages of our framework.
Weisheng Xu, Qiwei Wu, Jiaxi Zhang +7
Hong Kong University of Science and Technology (Guangzhou) · University of Oxford
Learning motion tracking from rich human motion data is a foundational task for achieving general control in humanoid robots, enabling them to perform diverse behaviors. However, discrepancies in morphology and dynamics between humans and robots, combined with data noise, introduce physically infeasible artifacts in reference motions, such as floating and penetration. During both training and execution, these artifacts create a conflict between following inaccurate reference motions and maintaining the robot's stability, hindering the development of a generalizable motion tracking policy. To address these challenges, we introduce OmniTrack, a general tracking framework that explicitly decouples physical feasibility from general motion tracking. In the first stage, a privileged generalist policy generates physically plausible motions that strictly adhere to the robot's dynamics via trajectory rollout in simulation. In the second stage, the general control policy is trained to track these physically feasible motions, ensuring stable and coherent control transfer to the real robot. Experiments show that OmniTrack improves tracking accuracy and demonstrates strong generalization to unseen motions. In real-world tests, OmniTrack achieves hour-long, consistent, and stable tracking, including complex acrobatic motions such as flips and cartwheels. Additionally, we show that OmniTrack supports human-style stable and dynamic online teleoperation, highlighting its robustness and adaptability to varying user inputs.
Yuhan Li, Peiyuan Zhi, Yunshen Wang +6
Huazhong University of Science and Technology · State Key Lab of General AI, Beijing Institute for General Artificial Intelligence (BIGAI) · Shanghai Jiao Tong University
General-purpose humanoid trackers can execute diverse references, but their zero-shot coverage depends on large embodied corpora that are costly to extend. Text-to-motion generators offer scalable supervision, yet models trained on human motion or retargeted data inherit a gap between kinematic plausibility and robot executability. Existing one-way pipelines fix either the generated corpus or the reward tracker. We introduce GenTrack, an online generator--tracker framework that alternates execution-grounded, group-relative generator alignment with tracker training on newly generated references; anchoring and rehearsal constrain drift. On Unitree G1, we evaluate GenTrack with ProtoMotions and SONIC backbones across three zero-shot tracking splits including public AMASS and LAFAN benchmarks, and a private out-of-distribution test set of 1,024 prompt-motion pairs in the wild. The online co-training strategy consistently produces generators that output more robot-executable motions with strong semantic alignment, and trackers with markedly broader zero-shot coverage and improved tracking accuracy, especially on out-of-distribution references. These results demonstrate that joint online post-training effectively narrows the executability gap between retargeted references and robot-native motion, advancing zero-shot humanoid control without additional data collection and beyond the limitations of a static reference pool.
Zeyu Ling, Xinyao Yu, Renye Yan +4
Zhejiang University · Peking University · Tencent +1