KungfuBot: Physics-Based Humanoid Whole-Body Control for Learning Highly-Dynamic Skills

Conference: NeurIPS 2025 arXiv: 2506.12851 Code: Project Page Area: Video Understanding Keywords: humanoid control, motion imitation, reinforcement-learning, adaptive tracking, sim-to-real

TL;DR

This paper proposes the PBHC framework, which enables a humanoid robot (Unitree G1) to learn highly dynamic whole-body skills such as kung fu and dance through a physics-aware motion processing pipeline and a bi-level optimization scheme for adaptive tracking factors. The approach achieves substantially lower tracking errors than existing methods and is successfully deployed on real hardware.

Background & Motivation

• High-dynamic motion imitation is extremely challenging: Existing humanoid motion imitation methods (ExBody, OmniH2O, etc.) are limited to low-speed, smooth motions and cannot handle highly dynamic behaviors such as kung fu kicks or spinning jumps.
• Physical feasibility of reference motions: Human motion sequences extracted from video may violate the robot's physical constraints (joint limits, dynamics), making it difficult for RL to converge when directly maximizing a tracking reward.
• Limitations of fixed tracking tolerances: Existing methods use a fixed tracking reward parameter (tracking factor \(\sigma\)), which cannot adapt to motions of varying difficulty — a large \(\sigma\) makes the reward insensitive to errors, while a small \(\sigma\) drives the reward toward zero.
• High cost of dataset preprocessing: H2O requires training a privileged policy to filter infeasible motions, and ExBody2 requires training an initial policy to assess motion difficulty — both are expensive prerequisite steps.

Method

Stage 1: Motion Processing Pipeline

1. Video Motion Extraction: GVHMR is used to estimate SMPL-format motion from monocular video; its gravity-aligned coordinate frame eliminates body tilt artifacts.

2. Physics-Aware Motion Filtering: Dynamic stability is assessed using the CoM–CoP distance. Let \(\bar{\mathbf{p}}_t^{\text{CoM}}\) and \(\bar{\mathbf{p}}_t^{\text{CoP}}\) denote the ground projections of the center of mass and center of pressure, respectively:

\[\Delta d_t = \|\bar{\mathbf{p}}_t^{\text{CoM}} - \bar{\mathbf{p}}_t^{\text{CoP}}\|_2 < \epsilon_{\text{stab}}\]

An \(N\)-frame sequence is considered stable if: ① both the first and last frames are stable; and ② the maximum number of consecutive unstable frames does not exceed threshold \(\epsilon_N\).

3. Contact Mask Estimation and Motion Correction: Contact masks are estimated from ankle displacement under a zero-velocity assumption:

\[c_t^{\text{left}} = \mathbb{I}[\|\mathbf{p}_{t+1}^{\text{l-ankle}} - \mathbf{p}_t^{\text{l-ankle}}\|_2^2 < \epsilon_{\text{vel}}] \cdot \mathbb{I}[p_{t,z}^{\text{l-ankle}} < \epsilon_{\text{height}}]\]

A vertical offset correction is applied to floating artifacts: \(\psi_{t,z}^{\text{corr}} = \psi_{t,z} - \Delta h_t\), where \(\Delta h_t = \min_{v \in \mathcal{V}_t} p_{t,z}^v\), followed by EMA smoothing to remove jitter.

4. Motion Retargeting: A differentiable inverse-kinematics optimization aligns end-effector trajectories while satisfying joint limits.

Stage 2: Adaptive Motion Tracking

Exponential Tracking Reward:

\[r(x) = \exp(-x / \sigma)\]

where \(x\) is the tracking error (e.g., joint angle MSE) and \(\sigma\) is the tracking factor. A large \(\sigma\) renders the reward insensitive to errors; a small \(\sigma\) drives the reward toward zero.

Bi-Level Optimization for the Optimal Tracking Factor: The selection of \(\sigma\) is formalized as a bi-level optimization problem:

\[\max_{\sigma \in \mathbb{R}_+} J^{\text{ex}}(\mathbf{x}^*), \quad \text{s.t.} \quad \mathbf{x}^* \in \arg\max_{\mathbf{x} \in \mathbb{R}_+^N} J^{\text{in}}(\mathbf{x}, \sigma) + R(\mathbf{x})\]

where the inner objective \(J^{\text{in}} = \sum_{i=1}^N \exp(-x_i/\sigma)\) represents the simplified cumulative reward, and the outer objective \(J^{\text{ex}} = \sum_{i=1}^N -x_i^*\) minimizes total tracking error. Solving this yields the optimal tracking factor equal to the mean optimal tracking error:

\[\sigma^* = \left(\sum_{i=1}^N x_i^*\right) / N\]

Adaptive Update Mechanism: An EMA estimate \(\hat{x}\) of the tracking error is maintained, and \(\sigma\) is dynamically tightened during training:

\[\sigma \leftarrow \min(\sigma, \hat{x})\]

\(\sigma\) is monotonically non-increasing: starting from a large initial value, it tightens progressively as the policy improves, forming a closed-loop feedback mechanism.

RL Training Framework

• Asymmetric Actor-Critic: The actor observes only proprioception and temporal phase; the critic additionally receives reference motion positions, root linear velocity, and randomized physical parameters.
• Vectorized Rewards: Each reward component \(r_i\) is paired with an independent value head \(V_i(\mathbf{s})\), avoiding inaccurate value estimation caused by scalar aggregation.
• Reference State Initialization (RSI): Time steps are randomly sampled from the reference motion for initialization, enabling parallel learning across different motion phases.
• Domain Randomization + Zero-Shot Transfer: Simulation physics parameters are varied; the policy is deployed directly to the real G1 robot without fine-tuning.

Key Experimental Results

Table 1: Main Tracking Performance Comparison (Mean ± Std, Bold = Best)

Method	\(E_{\text{g-mpbpe}}\)↓(mm)	\(E_{\text{mpbpe}}\)↓(mm)	\(E_{\text{mpjpe}}\)↓(\(10^{-3}\)rad)
Easy
OmniH2O	233.54±4.0	103.67±1.9	1805.1±12.3
ExBody2	588.22±11.4	332.50±3.6	4014.4±21.5
PBHC	53.25±17.6	28.16±6.1	725.6±16.2
Medium
OmniH2O	433.64±16.2	151.42±7.3	2333.9±49.5
ExBody2	619.84±26.2	261.01±1.6	3738.7±26.9
PBHC	126.48±27.0	48.87±7.6	1043.3±104
Hard
OmniH2O	446.17±12.8	147.88±4.1	1939.5±23.9
ExBody2	689.68±11.8	246.40±1.3	4037.4±16.7
PBHC	290.36±139	124.61±54	1326.6±379

PBHC consistently outperforms the deployable baselines (OmniH2O, ExBody2) across all difficulty levels and all metrics. On the Easy level, the global position error is reduced from 234 mm to 53 mm (a 77% reduction).

Table 2: Real-World Tai Chi Tracking Performance

Platform	\(E_{\text{mpbpe}}\)↓	\(E_{\text{mpjpe}}\)↓	\(E_{\text{mpbve}}\)↓	\(E_{\text{mpjve}}\)↓
MuJoCo	33.18±2.7	1061±83.3	2.96±0.34	67.71±6.7
Real	36.64±2.6	1130±9.5	3.01±0.13	65.68±2.0

Real-world metrics closely match simulation results, validating the effectiveness of zero-shot sim-to-real transfer.

Ablation Study

Fixed-\(\sigma\) configurations (Coarse/Medium/UpperBound/LowerBound) yield inconsistent performance across different motions — certain configurations perform well on specific motions but poorly on others. The adaptive mechanism consistently achieves near-optimal performance across all motion types.

Physical Filtering Effectiveness

Among 10 motion sequences subjected to filtering, 4 are rejected and 6 are accepted. Accepted motions all exhibit high Episode Length Ratios (ELR), while the highest ELR among rejected motions is only 54%, validating the effectiveness of the physical feasibility metric.

Highlights & Insights

• Theoretically elegant adaptive tracking factor: Formalizing \(\sigma\) selection as a bi-level optimization and deriving the closed-form solution \(\sigma^* = \text{mean error}\) eliminates the need for manual tuning.
• Demonstrated high-dynamic capability: Kung fu punches, 360° spinning kicks, and tai chi are successfully demonstrated on the real G1 robot.
• Complete motion processing pipeline: An end-to-end pipeline is established from video extraction → physics filtering → contact correction → retargeting.
• Zero-shot sim-to-real transfer: Successful deployment requires no real-world fine-tuning.

Limitations & Future Work

• One policy per motion: Each motion requires training an independent policy, which does not scale efficiently to large motion libraries.
• Lack of environment awareness: The system has no terrain perception or obstacle avoidance capability, limiting deployment in unstructured environments.
• Dependence on MoCap video quality: Motions extracted by GVHMR may be inaccurate; physical filtering mitigates this but is not comprehensive.
• High variance on Hard-level motions: The large standard deviations in tracking error for Hard motions indicate that stability remains an open challenge.

Related Work & Insights

• Humanoid motion imitation (DeepMimic [Peng+ 2018], ExBody2 [Ji+ 2024], OmniH2O [He+ 2024]): Prior methods are limited to low-speed motions; PBHC extends the capability frontier to highly dynamic behaviors.
• Humanoid whole-body control (HugWBC, ASAP [He+ 2025]): ASAP addresses the sim-to-real gap via multi-stage and residual policies, whereas PBHC resolves it entirely within simulation.
• Motion processing (IPMAN [Tripathi+ 2023], GVHMR [Shen+ 2024]): PBHC augments GVHMR with physics-aware filtering and contact correction.

Rating

• Novelty: ⭐⭐⭐⭐ — Solid theoretical contribution via bi-level optimization derivation of adaptive \(\sigma\); complete physics filtering pipeline.
• Experimental Thoroughness: ⭐⭐⭐⭐⭐ — Simulation comparisons + ablations + real-world deployment + quantitative sim-to-real validation.
• Writing Quality: ⭐⭐⭐⭐ — Clear mathematical derivations and systematic experimental organization.
• Value: ⭐⭐⭐⭐ — Substantially advances the frontier of highly dynamic skill learning for humanoid robots.

Related Papers

• [NeurIPS 2025] Adversarial Locomotion and Motion Imitation for Humanoid Policy Learning
• [CVPR 2026] Learning to Assist: Physics-Grounded Human-Human Control via Multi-Agent Reinforcement Learning
• [NeurIPS 2025] InFlux: A Benchmark for Self-Calibration of Dynamic Intrinsics of Video Cameras
• [NeurIPS 2025] FastVID: Dynamic Density Pruning for Fast Video Large Language Models
• [AAAI 2026] Coordinated Humanoid Robot Locomotion with Symmetry Equivariant Reinforcement Learning Policy