KungfuBot: Physics-Based Humanoid Whole-Body Control for Learning Highly-Dynamic Skills
Authors: Weiji Xie
Jinrui Han
Jiakun Zheng
Huanyu Li
Xinzhe Liu
Jiyuan Shi
Weinan Zhang
Chenjia Bai
Xuelong Li
Venue: NeurIPS 2025 poster ()
Keywords: Humanoid Robots
Whole-Body Locomotion
Motion Imitation
Primary area: reinforcement_learning
TL;DR: This paper presents a physics-based humanoid control framework, aiming to mastering highly-dynamic human behaviors such as Kungfu and dancing through physics-based motion selection and adaptive motion imitation.

Abstract: Humanoid robots are promising to acquire various skills by imitating human behaviors. However, existing algorithms are only capable of tracking smooth, low-speed human motions, even with delicate reward and curriculum design. This paper presents a physics-based humanoid control framework, aiming to master highly-dynamic human behaviors such as Kungfu and dancing through multi-steps motion processing and adaptive motion tracking. For motion processing, we design a pipeline to extract, filter out, correct, and retarget motions, while ensuring compliance with physical constraints to the maximum extent. For motion imitation, we formulate a bi-level optimization problem to dynamically adjust the tracking accuracy tolerance based on the current tracking error, creating an adaptive curriculum mechanism. We further construct an asymmetric actor-critic framework for policy training. In experiments, we train whole-body control policies to imitate a set of highly dynamic motions. Our method achieves significantly lower tracking errors than existing approaches and is successfully deployed on the Unitree G1 robot, demonstrating stable and expressive behaviors. The project page is https://kungfubot.github.io.

KungfuBot: Physics-Based Humanoid Whole-Body Control for Learning Highly-Dynamic Skills
Weiji Xie 1.2
Jinrui Han 12
Jiakun Zheng"
Huanyu Li Xinzhe Liu
Jiyuan Shi'
Weinan Zhang?
Chenjia Bait!
Xuelong Lit
Institute of Artificial Intelligence (TeleAI), China Telecom
Shanghai Jiao Tong University
'East China University of Science and Technology
Harbin Institute of Technology SShanghaiTech University
Abstract
Humanoid robots are promising to acquire various skills by imitating human behaviors. However, existing algorithms are only capable of tracking smooth, low-speed human motions, even with delicate reward and curriculum design. This paper presents a physics-based humanoid control framework, aiming to master highly-dynamic human behaviors such as Kungfu and dancing through multi- steps motion processing and adaptive motion tracking. For motion processing, we design pipeline to extract, filter out, correct, and retarget motions, while ensuring compliance with physical constraints to the maximum extent. For motion imitation, we formulate bi-level optimization problem to dynamically adjust the tracking accuracy tolerance based on the current tracking error, creating an adaptive curriculum mechanism. We further construct asymmetric actor-critic framework for policy training. In experiments, we train whole-body control policies to imitate set of highly-dynamic motions. Our method achieves significantly lower tracking errors than existing approaches and is successfully deployed on the Unitree G1 robot, demonstrating stable and expressive behaviors. The project page is sojhttps://kunee bot. githubtthh.......
1 Introduction
Humanoid robots, with their human-like morphology, have the potential to mimic various human behaviors performing different tasks []] The ongoing advancement motion capture (Mo- Cap) systems and motion generation methods has led to the creation of extensive motion datasets 31, which encompass a multitude of human activities annotated with textual descriptions [4. Consequently, it becomes promising for humanoid robots to learn whole-body control to imitate human behaviors. However, controlling diggh-dimessonal robot actions to achieve ideal human like performance presents substantial challenge. One major difficulty arises from the fact that motion sequences captured from humans may not comply with the physical constraints of humanoid robots, including joint limits, dynamics, and kinematics [5) 6 Hence, directly training policies through Reinforcement Learning (RL) to maximize rewards (e.g., the negative tracking error) often fails to yield desirable policies, as it may not exist within the solution space.
Recently, several RL-based whole-body control frameworks have been proposed to track motions 7 3, which often take reference kinematic motion as input and output the control actions for a humanoid robot to imitate it. To address physical feasibility issues, H2O and OmniH20 9 [0] remove the infeasible motions using trained privileged imitation policy, producing clean motion
"Equal contributions. Correspondence to: Chenjia Bai (baicj@ chinatelecom.cn)
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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dataset. ExBody 77] constructs a feasible motion dataset by filtering via language labels, such as 'wave' and 'walk'. Exbody2 [S] trains an initial policy on all motions and uses the tracking error to measure the difficulty of each motion. However, it would be costly to train the initial policy and find an optimal dataset. There also a lack of suitable tolerance mechanisms for difficult-to-track motions in the training process. As result, previous methods are only capable of tracking low-speed and smooth motions. Recently, ASAP [6] introduces a multi-stage mechanism and learned a residual policy to compensate for the sim-to-real gap, reducing the difficulties in tracking agile motions. Unlike ASAP, we focus on improving motion feasibility and agility entirely in simulation.
In this paper, we propose Physics-Baas Based Humanoid motion Control (PBHC), which utilizes a two-stage framework to tackle the challenges associated with agile and highly-dynamic motions. (i) In the motion processing stage, we first extract motions from videos and establish physics-base based metrics to filter out human motions by estimating physical quantities within the human model, thereby eliminating motions beyond the physical limits. Then, we compute contact masks of motions followed by motion correction, and finally retarget processed motions to the robot using differential inverse kinematics. (īi) In the motion imitation stage, we propose an adaptive motion tracking mechanism that adjusts the tracking reward via a tracking factor. Perfectly tracking hard motions is impractical due to imperfect reference motions and the need of smooth control, so we adapt the tracking factor to different motions based on the tracking error. We then formulate a Bi-Level Optimization (BLO) [ to derive the optimal factor and design an adaptive update rule that estimates the tracking error online to dynamically refine the factor during training.
Building on the two-stage framework, we design an asymmetric actor-critic architecture for policy optimization. The critic adopts a reward vectorization technique and leverages privileged information to improve value estimation, while the actor relies solely on local observations. In experiments, PBHC enables whole-body control policies to track highly-dynamic motions with lower tracking errors than existing methods. We further demonstrate successful real-world deployment on the Unitree GI robot, achieving stable and expressive behaviors, including complex motions like Kungfu and dancing.
2 Preliminaries
Problem Formulation. We adopt the Unitree G1 robot [2] in our work, which has 23 degrees of freedom (DoFs) to control, excluding the DoFs in each wrist of the hand. We formulate the motion imitation problem as goal-conditional RI. problem with Markov Decision Process r. P), where S and gref are the state spaces of the humanoid robot and refer- ence motion, respectively, A is the robot's action space, is mixed reward function consisting motion-tracking and regularization rewards, and P is the transition function depending on the robot morphology and physical constraints. At each time step the policy π observes the proprioceptive of the robot and generates action as, with the aim of obtaining the next-state 8141 that fol- state s prop
M = AS, Svef, A,
lows the corresponding reference state sfef in the reference trajectory [s ...., s The action a, E 28 is the target joint position for a PD controller to compute the motor torques. We adopt an off-the-shelf RL algorithm, PPO [3] for policy optimization with actor-critic architecture
Reference Motion Processing. For human motion processing, the Skinned Multi-Person Linear (SMPL) model [14] offers a general representation of human motions, using three key parameters: B 10 for body shapes. 0 E 24x33 for joint rotations in axis-angle representation, and sb E R for global translation. These parameters can be mapped to 3D mesh consisting of 6,890 vertices via differentiable skinning function M-),, which formally expressed as = M(9 O, ab) E R8690033 We employ a human motion recovery model to estimate SMPL parameters (B, O, {b) from videos, followed by additional motion processing. The resulting SMPL-format motions are then retargeted to GI through an Inverse Kinematics (IK) method, yielding the reference motions for tracking purposes.
3 Methods
An overview of PBHC is illustrated in Fig. [ First, raw human videos are processed by a Human Motion Recovery (HMR) model to produce SMPL-format motion sequences. These sequences are filtered via bassics-based metrics and corrected using contact masks. The refined motions are then retargeted to the GI robot. Finally, each resulting trajectory serves as reference motion for training a separate RL policy, which is then deployed on the real G1 robot. In the following, we detail the motion processing pipeline ($3.1) adaptive motion tracking module ($3.2 and RL framework (.3..

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(4) Multi-Steps Motion Processing
(b) Adaptive Motion Tracking
Human Video
Reference Trajectory & Contact Mask
ref
l/g,
Qrlla
Update
lp P.112
state
1|
8:lla
Optimize
(c) RL Training Framework
observation
Simulation
Policy
Motion Estimatiin
action
IK-based Retargeting & Contact Mask Extraction
Physics
Deploy
Based Motion
Filtering
Feasible Motions
An overview of PBHC that includes three core components: (a) motion extraction from videos and multi-steps motion processing, (b) adaptive motion tracking based on the optimal tracking factor, (c) the RL training framework and sim-to-real deployment.
Figure 1:
3.1 Motion Processing Pipeline
We propose motion processing pipeline to extract motion from videos for humanoid motion tracking, comprising four steps: (i) SMPL--forma motion estimation from monocular videos, (ii) physics- based motion filtering, (iii) contact-aware motion correction, and (iv) motion retargeting. This pipeline ensures that physically plausible motions can be transferred from videos to humanoid robots.
Motion Estimation from Videos. We employ GVHMR [5] to estimate SMPL-format motions from monocular videos. GVHMR introduces a gravity- view coordinate system that naturally aligns motions with gravity, eliminating body tilt issues caused by reconstruction solely relying on the camera coordinate system. Furthermore, it mitigates foot sliding artifacts by predicting foot stationary probabilities, therehy enhancing motion quality.
Physics-based Motion Filtering. Due reconstruction inaccuracies and out-of-distributin issues in HMR models, motions extracted from videos may violate physical and biomechanical constraints. Thus, we try filter out these motions via physics-based principles. Previous work (16) suggests that proximity between the center of mass (CoM) and center of pressure (CoP) indicates greater stability, and proposes method estimate CoM and CoP coordinates from SMPL data. Building on this,
calculate the projected distance of CoM and CoP on the ground for each frame and apply a threshold to assess stability. Specifically, let p. 2
CoP denote the CoM Pi.y CoM) and pCoP CoCoP p.
projected coordinates of CoM and CoP on the ground at frame t respectively, and Ad, represents the distance between these projections. We define the stability criterion of frame
Ad, 1 |ICCoM
Pr
CoP < <stab:
(1)
where Estab represents the stability threshold. Then, given N-frame motion sequence, let B [to, $i...., .....,ty tx] be the increasingly sorted list of frame indices that satisfy Eq. I where t& E [1, Nj. The motion sequence is considered stable if it satisfics two conditions: (i) Boundary -fame stability: 1 E B and e B. (ii) Maximum instability gap: the maximum length of consecutive unstable frames must be less than threshold cn, i.e., max; f++1 tx eN. Based this criterion, motions that clearly unable to maintain dynamic stability can be excluded from the original dataset.
Motion Correction based on Contact Mask. To better capture foot-ground contact in motion data, we estimate contact masks by analyzing ankle displacement across consecutive frames, based on zero-velocity assumption [17 18) Let pl-ankle E IR'S denote the position of the left ankle joint at time
t, and cleft E {0,1] the corresponding contact mask. The contact mask is estimated as
left
1[] Pt+1
laanle
1aankle 12 Evel] Lankallle
Cheight]:
(2)

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where Evel and hhiggtt are empirically chosen thresholds. Similarly for the right foot.
To address minor floating artifacts not eliminated by threshold-based filtering, we apply a correction step based on the estimated contact mask. Specifically, if either foot is in contact at frame i, a vertical offset is applied to the global translation. Let ab denotes the global translation of the pose at time t, then the corrected vertical position is:
Corr 11, h1:
where Ah, min Př, is the lowest c-coordinate among the SMPL mesh vertices V; at frame t. While the correction alleviates floating artifacts, it may cause frame-to-frame jitter. We address this by applying Exponential Moving Average (EMA) smooth the motion.
Motion Retargeting. We adopt an inverse kinematics (IK)-based method [19 to retarget processed SMPL-format motions to the GI robot. This approach formulates differentiable optimization problem that ensures end-effector trajectory alignment while respecting joint limits.
To enhance motion diversity, we incorporate additional data from open-source datasets, AMASS and LAFAN (0).. These motions are partially processed through our pipeline, including contact mask estimation, motion correction, and retargeting.
4
3.2
Adaptive Motion Tracking
3.2.1
Exponential Form Tracking Reward
The reward function in PBHC, detailed in Appendix C.2 comprises two components: task-specific rewards, which enforce accurate tracking of reference motions, and regularization rewards, which promote overall stability and smoothness.
The task-specific rewards include terms for aligning joint states, rigid body state, and foot contact mask. These rewards, except the foot contact tracking term, follow the exponential form
r r(x) = exp(-z/o)
where æ represents the tracking error, typically measured as the mean squared error (MSE) of quantities such as joint angles, while controls the tolerance of the error, referred to as the tracking factor. This exponential form is preferred over the negative error form because it is bounded, helps stabilize the training process, and provides more intuitive approach for reward weighting.
Intuitively, when a is much larger than the typical range of x, the reward remains close to 1 and be- comes insensitive to changes in ı, while an overly small causes the reward approach and also reduces its sensitivity, highlighting the importance of choosing a appropriately to enhance responsive- ness and hence tracking precision. This intuition is illustrated in Fig.
exp z(a)
Effect of Tracking Factor Reward
1.00-
0.2
0.75
6.0
Range
0.50
Mean Erso
0.25
Reward
0.0
0.5
1.0
1.5
2.0
2.5
Tracking Error 2
3.2.2 Optimal Tracking Factor
Illustration of the effect of tracking factor o on the reward value.
Figure 2:
To determine the choice of the optimal tracking factor, we introduce a simplified model of motion tracking and formulate it as bi-level optimization problem. The intuition behind this formulation is that the tracking factor should be chosen to minimize the accumulated tracking error of the converged policy over the reference trajectory. In manual tuning scenarios, this is typically achieved through an iterative process where an engineer selects a value for a, trains a policy, observes the results, and repeats the process until satisfactory performance is attained.
Given a policy ~ there is a sequence of expected tracking error x R for N steps, where o. represents the expected tracking error at the i-th step of the rollout episodes. Rather than optimizing the policy directly, we treat the tracking error sequence æ as decision variables. This allows to reformulate the optimization problem of motion tracking as:
max J [x, .) + +(xx, ΦERY
(5)
4

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i= exp(-z;/o) is the simplified accumulated reward induced by the tracking reward in Eq. 4. and we introduce R(z) to capture all additional effects beyond J including environment dynamics and other policy objectives such as extra rewards. The solution x" to Eq. (5) corresponds to the error sequence induced by the optimal policy n². Subsequently, the optimization objective of a is to maximize the obtained accumulated negative tracking error jxx(x*) E 27 the external objective, formalized the following bi-level optimization problem:
where the internal objective J (x( E
(*"), s.t. x² arg max (a R(x). sER;
max oERt
(6)
This simplified modeling provides an intuitive connection to the RL training process.
The lower-level optimization represents the standard RL procedure, where a policy is trained to maximize tracking reward and other reward terms, given specific a.
The upper-level optimization, outside the RL loop, selects a to minimize the total tracking error of the final converged policy. This outer optimization is not reward maximization but performance-drivel objective based on absolute external metrics.
Under additional technical assumptions, can solve Eq. (6) and derive that the optimal tracking factor is the average the optimal tracking error, as detailed in Appendix
Σ i=1 23 IN.
3.2.3 Adaptive Mechanism
12
Strage Haw (006--4)
Reward r(z) Shaping
Tracking Factor o Tightening
Poritoo (M0)
Sikcoge Boop 3ih--
Policy Optimization
Tracking Error Reduction
Quick Punch
20
26
Tanc (4)
Figure 3:
Closed-loop adjustment of tracking factor in the proposed adaptive mechanism.
Figure 4: Example of the right hand y-position for 'Horse-stance punch'. The adaptive a can progressively improve the tracking precision. Ppoe_r is used for tracking the head and hands.
While Eq. (7) provides a theoretical guidance for determining the tracking factor, the coupling between o* and x" creates a circular dependency that prevents direct computation. Additionally, due the varying quality and complexity of reference motion data, selecting single, fixed value for the tracking factor that works for all motion scenarios is impractical. To resolve this, we design an adaptive mechanism that dynamically adjusts o during training through feedback loop between eтror estimation and tracking factor adaptation.
In this mechanism, we maintain Exponential Moving Average (EMA) & of the instantaneous tracking error over environment steps. This EMA serves as an online estimate of the expected tracking under the current policy, and during training this value should approach the average optimal tracking error (EN,>) #t) /N under the current factor a. At each step, PBHC updates to the
current value of &, creating a feedback loop where reductions in tracking error lead to tightening of a. This closed-looe loop process drives further policy refinement, and as the tracking error decreases, the system converges to an optimal value of that asymptotically solves Eq. 99. as illustrated Fig.
To ensure stability during training, we constrain to be non-increasing and initialize it with relatively large value, ginit The update rule is given by Eq. (8) As shown in Fig. this adaptive mechanism allows the policy to progressively improve its tracking precision during training.
a min(a, 2).
(8)
5

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3.3 RL Training Framework
Asymmetric Actor-Critic. Following previous works [1] the time phase variable Φ E [0. is introduced to represent the current progress of the reference motion linearly, where de denotes the start of a motion and di = denotes the end. The observation of the actor gector includes the robot's proprioception is sp and the time phase variable dt. The proprioception sprrpp qu- 4:-4: 4:t; w/-4:t: Pi- Q1-3:t1] includes 5-step history of joint position q: E I joint velocity ÿ: E IR28 root angular velocity wo E R2, root projected gravity g, E IR33 and last-step action - R223, The critic receives an augmented observation s. sprtie, including s.. s.rop, time phase, reference motion positions, root linear velocity, and set of randomized physical parameters.
Reward Vectorization. To facilitate the learning of value function with multiple rewards, we vectorize rewards and value functions as: r = [ri....,FTr and (s) = (V)()),... V (8)) following Xie al. [22). Rather than aggregating all rewards into a single scalar, each reward component is assigned to a value function (s(s) that independently estimates returns, implemented by a critic network with multiple output heads. All value functions are aggregated to compute the action advantage. This design enables precise value estimation and promotes stable policy optimization.
Reference State Initialization. We use Reference State Initialization (RSI) (21, which initializes the robot's state from reference motion states at randomly sampled time phases. This facilitates parallel learning of different motion phases, significantly improving training efficiency.
Sim-to-Real Transfer.
To bridge the sim-to-real gap, we adopt domain randomization by varying the physical parameters of the simulated environment and humanoids. The trained policies are validated through sim-to-sim testing before being directly deployed to real robots, achieving zero-shot sim-to-real transfer without any fine-tuning. Details are in Appendix C
4 Related Works
Humanoid Motion Imitation. Robot motion imitation aims to learn lifelike and natural behaviors from human motions [3] Although there exist several motion datasets that contain diverse mo- tions (24 25 4] humanoid robots cannot directly learn the diverse behaviors due to the significantly different physical structures between humans and humanoid robots 66 Mcanwhile, most datasets lack physical information, such as foot contact annotations that would be important for robot policy As a result, we adopt physics- -based motion processing for motion filtering and contact annotation. After obtaining the reference motion, the humanoid robot learns wodle-body control policy to interact with the simulator 22 30), with the aim of obtaining a state trajectory close to the reference 31 (2]
learning 27 28
However, learning such a policy is quite challenging. the robot requires precise control of high-dimensional DoF's to achieve stable and realistic movement 7 g. Recent advances adopt physics-based motion filtering and RL to learn whole-body control policies [5] and perform real-world adaptation via sim-to-real transfer [33]. However, because of the lack of tolerance mechanisms for hard motions, these methods are only capable of tracking relatively simple motions. Other works also combine telcoperation [34] 35) and independent control of upper and lower bodies (36), while they may sacrifice the expressiveness of motions. contrast, we propose an adaptive mechanism to dynamically adapt the tracking rewards for agile motions.
Humanoid Whole-Body Control. Traditional methods for humanoid robots usually learn indepen- dent control policies for locomotion and manipulation. For the lower-body, RL-based controller have been widely adopted to learn locomotion policies for complex tasks such as complex-terret -terran walking
337 388, gait control (39,, standing up 40 41], jumping (42), and even parkour [43 44 However,
each locomotion task requires delicate reward designs, and human-like behaviors are difficult obtain [45] 466. In contrast, we adopt human motion as references, which is straightforward for robots to obtain human-liks behaviors. For the upper-body, various methods propose different architectures to learn manipulation tasks, such as diffusion policy [7 48
model 49 50 [1],
dual-system architecture [52] (33, and world models [54 55]. However, these methods may overlook the coordination of the two limbs. Recently, several whole-body control methods have been proposed,
with the aim of enhancing the robustness of entire systems in locomotion [2 39 34 or performing
[56]. Differently, the upper and lower bodies of our method have the same objective to track the reference motion, while the lower body still requires maintaining stability and preventing falling in motion imitation. Other methods collect whole-body control datasets to learn
loco-manipulation tasks

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Horse-stance punch (Easy)
Stretch leg (Medium)
Jump kick (Medium)
360-degree spin (Hard)
Figure 5: Example motions in our constructed dataset. Darker opacity indicates later timestamps.
humanoid foundation model 56 57. while requiring large number of trajectories. In contrast, we only require small number of reference motions learn diverse behaviors.
5
Experiments
In this section, we present experiments to evaluate the effectiveness of PBHC. Our experiments aim answer the following key research questions:
Q1. Can our physics- based motion filtering effectively filter out untrackable motions?
Q2. Does PBHC achieve superior tracking performance compared prior methods in simulation?
Q3. Does the adaptive motion tracking mechanism improve tracking precision?
Q4. How well does PBHC perform in real-world deployment?
5.1 Experiment Setup
100%
Evaluation Method. We assess the policy's tracking per- formance using highly-dynamic motion dataset constructed through our proposed motion processing pipeline, detailed in Appendix B Examples shown in Fig. [] We categorize motions into three difficulty levels: easy, medium, and hard, based their agility requirements. For each setting, policies are trained in IsaacGym (29] with three random seeds and are evaluated over 1,000 rollout episodes.
Episede Lengili Ratio (%5
Metrics. The tracking performance of polices is quantified through the following metrics: Global Mean Per Body Position Error (Eg-mpboe. mm), root-relative Mean Per Body Position Er- ror (Emphpe, mm), Mean Per Joint Position Error (Empipe 10-3 rad), Mean Per Joint Velocity Error (Empive: 10-3 rad/frame), Mean Per Body Velocity Error (Fmphwe, mm/frame), and Mean Per Body Acceleration Error (Emptues mm/frame²). The defini- tion of metrics is given in Appendix D.2]
Accepted motion Rejected motion
Figure 6: The distribution of ELR of accepted and rejected motions.
5.2 Motion Filtering
To address Q1, we apply our physics-basd basicd motion filtering method (see $3.1) to 10 motion sequences. Among them, sequences rejected based the filtering criteria, while the remaining are accepted. To evaluate the effectiveness the filtering, we train a separate policy for each motion and compute the Episode Length Ratio (ELR), defined the ratio of average episode length to reference motion length.
As shown in Fig. 0 accepted motions consistently achieve high ELRs, demonstrating motions that satisfy the physics-based metric can lead to better performance motion tracking. In contrast, rejected motions achieve maximum ELR of only 54%, suggesting frequent violations of termination conditions. These results demonstrate that our filtering method effectively excludes inherently untrackable motions, thereby improving efficiency by focusing viable candidates.

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Table 1: Main results comparing different methods across difficulty levels. PBHC consistently outperforms deployable baselines and approaches oracle-level performance. Results are reported as mean + one standard deviation. Bold indicates methods within one standard deviation of the best result, excluding Oracle baselines. Asterisks (*) denote significant improvements (p < 0.05) of our method over baselines per two-sided permutation tests.
Method
Eggmmphpe
Emplin
Empipe
Emphive +
Emppoas
Empipe
Easy
OmniH20
233.54_4.003
103.67
1805.10
8.54
8.46g008i
224.70+2044
ExBody2
588, 211.42
4014,40 333.50
14.29
9.80
206. +1.56
Ours
53.25
28.16
725.62 16:00
4,41
4.65
81.28
MaskedMinic (Oricce
411.79 41.79
21 2,000
"139.90 19.4
5,20
7
7,30
T32. 25.91
Ours (Oracle)
45.022..700
22.
100.30
4.63
4.89 2099
23.44
Medium
OmniH20
433.64.1661
151,4227300
2333. g4.3.9
10.85
10,54
204.36
ExBody2
619.84-2616
261 21.00
3738.70
14.48
11.25
204.33+22122
Ours
126.48.27011
48-87
1043.30
4 104.4
6.62
105.30 109.30,394
MaskedMinic (Oracle)
150.92
61. 61.69144.
8.16 .914
10.01 10.01 2038t
174684
Ours (Oracle)
g6.85
29.56.14.53
753.69
100.2
5.34
6.58
82. 92.73
Hard
OmniH20
446. 446.17 =7
147.88
1939.50+22.90
14.98
14.40
190. 4
ExBody2
689.68.1130
246.40
4037.40 11070
19,90
16. 16.722m.00
254.76 a.
Ours
290.36
124.61 455.54
1326.60 +378.9
11.93-2.02
12.36
135.05 1 43.43
MaskedMinic (Oracle)
47.744.2702
27. 27.25
829.02..1541
2..3
10. 10.602.4400
146. 13.322
Ours (Oracle)
79.25
34.742026
734.90
2.04
1.34
93.79
5.3 Main Result
To address Q2, we compare PBHC with three baseline methods: OmniH20 [10], Exbody2 [5], and
MaskedMimic (23). All baselines employ the exponential form of the reward function for tracking reference motion, as described in $3.2.1 Implementation details are provided in Appendix D.3
As shown in Table I PBHC consistently outperforms the baselines OmniH20 and ExBody2 across all evaluation metries. These improvements can be attributed to our adaptive motion tracking mechanism, which automatically adjusts tracking factors based on motion characteristics, whereas the fixed, empirically tuned parameters in the baselines fail to generalize across diverse motions. While MaskedMimic performs well on certain metrics, it is primarily designed for character animation and not deployable for robot control, as it does not account for constraints such as partial observability and action smoothness. To enable a fair comparison, we also train an oracle version of PBHC that similarly overlooks such constraints, the same manner as MaskedMimic.
5.4 Impact of Adaptive Motion Tracking Mechanism
To investigate Q3, we conduct an ablation study evaluating our adaptive motion tracking mecha- nism ($3.2) against four baseline configurations with fixed tracking factor set: Coarse, Medium, UpperBound, LowerBound. The tracking factors in Coarse, Medium, UpperBound, and LowerBound are roughly progressively smaller, with LoverBound approximately corresponding to the smallest tracking factor derived from the adaptive mechanism after training convergence, while UpperBound approximately corresponds to the largest. The specific configuration of baselines and the converged tracking factors of the adaptive mechanism are given in Appendix D.4
As shown in Fig. 7 the performance of the fixed tracking factor configurations (Coarse, Medium, LowerBound and UpperBound) varies between different motion types. Specifically, while Lower- Bound and UpperBound achieve strong performance on certain motions, they perform suboptimally on others, indicating that no single fixed setting consistently yields optimal tracking results on all motions. In contrast, our adaptive motion tracking mechanism consistently achieves oparmol performance across all motion types, demonstrating its effectiveness in dynamically adjusting the tracking factor to suit varying motion characteristics.
8

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Bupipe
Eagipe
Eypipe
Empipe
Euphpo Eaptes
Expter
Emphpe Exples
Eagloe
Emplon
Eig Eappheee
Egmphpp
Empose a) Jabs punch
Empiye
Empjoe
Empnon
b) Charleston dance
c) Roundhouse kick
d) Bruce Lee's pose
Ours
Counee
Medium
Upperbound
Lowerbound
Figure 7: Ablation study comparing the adaptive motion tracking mechanism with fixed tracking factor variants. The adaptive mechanism consistently achieves near-optimal performance across all motions, whereas fixed variants exhibit varying performance depending on motions.
Horse-stance punch
Stretch
c) Jabs punch
Tal Chi
Jump kick
Bruce Lee's pose
Roundhouse kick
h)) 360-degree spin
Front kick
j) Charleston dance
Figure 8: Our robot masters highly-dynamic skills in the real world. Time flows left to right.
5.5 Real-World Deployment
To investigate Q4, we deploy the policies in real robot. As shown in Fig. and the supporting videos, our robot in real world demonstrates outstanding dynamic capabilities through diverse repertoire advanced skills: (1) sophisticated martial arts techniques including powerful boxing combinations (jabs, hooks, and horse-stance punches) and high-degree kicking maneuvers (front kicks, jump kicks, side kicks, back kicks, and spinning roundhouse kicks); (2) acrobatic movements such as full 360-degree spins; (3) flexible motions including deep squats and stretches; (4) artistic per- formances ranging from dynamic dance routines to graceful Tai Chi sequences. This comprehensive skill set highlights system's 's remarkable versatility, dynamic control, and real-world applicability across both athletic and artistic domains.
To quantitatively assess our policy's tracking performance, we conduct 10 trials of the Tai Chi motion and compute evaluation metrics based on the onboard sensor readings, as shown Table Notably, the metrics obtained in the real world are closely aligned with those from the sim-to-sim platform MuJoCo, demonstrating that our policy can robustly transfer from simulation to real-world deployment while maintaining high-performanee control.

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Table 2: Comparison of tracking performance of Tai Chi between real-world and simulation. The robot root is fixed the origin since it's inaccessible real-world.
Platform Empbpe
Empipe J
Empbve
Empbae +
Empive
MuJoCo 33. 13.1822.720
1061.24483..
2.96403342
2.90
67.71 65.68.+1.922
Real
36.6442.592
1130.05
3.01
3.1250.056
5.6 Learning Curves
To additionally illustrate the training process and verify its stability, present in Fig. the learning curves for three representative motions-Jabs Punch, Tai Chi, and Roundhouse Kick shoking both the mean episode length and mean reward. These curves provide intuitive view of how the policy improves over time, and can be observed that training gradually stabilizes and converges after approximately 20k steps, demonstrating the reliability and efficiency of our approach in learning complex motion behaviors.
500
25
punch
Jobs punch
Tai Chi
Tai Chi
Roundhouse kick
Roundhouse kick
Episode Lenghh
300
Reward 55
200-
Training Steps (k)
Training Steps (k)
Figure 9: Mean episode length and mean reward across three motions. Both curves indicate that training gradually stabilizes after 20k steps.
6 Conclusion & Limitations
This paper introduces PBHC, a novel RL framework for humanoid whole-body motion control that achieves outstanding highly-dynamic behaviors and superior tracking accuracy through physics-base based motion processing and adaptive motion tracking. The experiments show the motion filtering metric can efficiently filter trajectories that are difficult to track, and the adaptive motion tracking method consistently outperforms baseline methods on tracking eтror. The real-world deployments demonstrate robust behaviors for athletic and artistic domains. These contributions push the boundaries of humanoid motion control, paving the way for more agile and stable real-world applications.
However, method still has limitations. (i) It lacks environment awareness, such terrain perception and obstacle avoidance, which restricts deployment in unstructured real-world settings. (ii) Each policy is trained imitate single motion, which may not be efficient for applications requiring diverse motion repertoires. We leave research on how to maintain high dynamic performance while enabling broader skill generalization for the future.
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Acknowledgments and Disclosure of Funding
This work is supported by the National Key Research and Development Program of China (Grant No. (0,2024FFE2000000) Shanghai Municipal Science and Technology Major Project (Grant No. SH22D200222 the National Natural Science Foundation of China (Grant No. 62.62236222 and No. No.62322603), the Young Elite Scientists Sponsorship Program by CAST (Grant No.20240NRC001) and the Yangfan Project the Shanghai (Grant 14622000)
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Answer:
[NA]
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Please refer LLM policy should or should be described.
http:ppp..e///ooeeeerre///////// for what
20

---

A Derivation of Optimal Tracking Sigma
We recall the bi-level optimization problem in 6
max
J=""("
(9a)
DER
S.t.
x' E arg max (x, σ) + R(x))
(9b)
MERY
Assuming R(x)) takes lincar form R(a) Ar + b, J and J are twice continuously differentiable and the lower-level problem Eg, (9b) has unique solution x" (o). Then we take an implicit gradient approach to solve it. The gradient of se w.r.l. is:
d_jex dæ (a) V (x
(10)
do do
To obtain (a) de since x² (a) is lower-level solution, satisfies:
V=(J"(w"(o) R(x)) 0.
(11)
Take the first-order derivative of Eq. 11 w.r.t. then we have:
d
V (J
(x (o). + R(x)) Vonuth + do
dx - =0,
(12)
do
dæ (a)
v2 Ja (x=" (a), o) 0. (x'
(13)
do
Substituting Eq.
13 into Eq.
10
we have
d
V
(x
(o), ()) (x
(14)
do
om
where
N J=x(x)
Di,
(15a)
1=1 N
jdm (w σ)
exp( (xp(-1./o)..
(15b)
Compute first- and second-order gradients in Eq.
14
V VaJ (x, exp(-2x/)) x/a0( 0
(16a)
Va (x) 1,
(16b)
2 n (x. σ) a- x V a.a (0
exp( w/o0).
(16c)
diag(exp(-z/o)))
(16d)
where means element-wise multiplication. Substituting d
16 into
14
and let the gradient equals to zero
de 0, then we have
Ee 1
(17)
N
B Dataset Description
Our dataset integrates motions from: (i) video-basee sources, from which motion data is extracted through our proposed multi-steps steps motion processing pipeline. The hyperparameters of the pipeline listed in Table 3 (ii)
21

---

open-source datasets: selected motions from AMASS and LAFAN. The dataset comprises 13 distinct motions. which are categorized into three difficulty levels easy, medium, and hard. To ensure smooth transitions, linearly interpolate at beginning and end each sequence move from a default pose to the reference motion and back. The details are given in Table 4
Table 3: Hyperparameters of multi-steps motion processing.
Hyperparameter
Value
Estab
0.1
eN
100
Gvel
0.002
thoight
0.2
Table 4: The details the eighlydynammi motion dataset.
Motion name
Motion frames
Source
Easy
Jahs punch
285
video
Hooks punch
175
video
Horse-stance
210
LAFAN
Horse-stance punch
200
video
Medium
Stretch
320
video
Tai Chi
500
video
Jump kick
145
video
Charleston dance
610
LAFAN
Bruce Lee's pose
330
AMASS
Hard
Roundhouse kick
158
AMASS
360-degree spin
180
video
Front kick
155
video
Side kick
179
AMASS
C
Algorithm Design
C.1 Observation Space Design
Actor observation space: The actor's observation getor includes 5-step history of the robot's proprioceptive state s! grop and time-phase variable de.
Critic observation space: The critic's observation sitiic additionally includes the base linear velocity, the body position of the reference motion, the difference hetween the current and reference body positions, and of domain-randomized physical parameters. The details are given Table
Table 5: Actor and critic observation state space.
State term
Actor Dim
Critic Dim
Joint position
23 x
23 x
Joint velocity
23
Root angular velocity
3
3
Rool projected gravily
x
x
Reference motion phase
x
1 x
Actions
23 x 5
23 x
Root linear velocity
x
Reference body pusition
81
Body position difference
81
Randomized buse CoM officet*
Randoriized link m
22
Randomized stiffines**
Randomized dumping*
Randomized friction coefficient Randomized control delay
Total
22

---

*Severul rundomized physical parameters used in domain randomization are part of the critic observation to improve value extimation robustness. The detailed settings domain randomization are given in Appendix
C.2 Reward Design
All reward functions are detailed in T Our reward design consists of two main parts: task rewards and regularization rewards. Specifically, impose penalties when joint position exceeds the soft limits, which symmetrically scaled from the hard limits by a fixed ratio (a 0.95):
(quin Tmax /2,
(18a)
qmax - qmin:
(18b)
Quott-min m - 0.5 d ax;
(18c)
Qott-mnax m+ 0.5 d a,
(18d)
where q is the joint position. The same procedure is applied to compute the soft limits for joint velocity q and torque T.
Table 6: Reward terms and weights.
Term
Expression
Weight
Task
Joint position
exp( 1|q. 4:13 (pos)
Joint velocity
exp( 1/: 9: 9:113 (d
1.0
Body position
exp(- [p: 3 p/pp)))
Body rotation
exp( 1 (|p-- e 1/11///ro0
0.5
Body velocity
exp( (1--lle, 0/112/0
0.5
Body angular velocity
exp(-lles ||- W. 2 s/angg)
0.5
Body position 3 points
exp(- P P5 1 11//0poo Upon vr)
Body position feet
exp
lpp
p!
2/ foet)
1.0
Max Joint position
exp
||
Omaxx ipss))
Contact Musk
1 ||c 2//11/2
0.5
Regularization
Joint position limits
I(q [4soft-min: msoft-max)
11.00
Joint velocity limits
I(4 Iâsoft-min: 4soft-max) ))
Joint torque limits
1(7 & [Tooft-min Troft-cnax.)
-5.0
Slippage
fees ffot [|2 1]
Feet contact forces
min 400
-0.01
Feet time
[[Tare > 0.3]
Stumble
> 5 Fdeet)
-2.0
Torque
|
-lc-6
Action rate
||a 11
-0.02
Collision
Icollision
-30
Termination
terminattinn
-200
C33 Domain Randomization
To improve the transferability of our trained polices to real-world settings, we incorporate domain randomization during training support robust sim-to- tim-to-sim and sim-to-real transfer. The specific settings given in Table
C.4 PPO Hyperparameter
The detailed PPO hyperparameters shown in Table
23

---

Table 8: Hyperparameters related to PPO.
Table 7: Domain randomization settings,
Hyperparameter
Value
Torm
Value
Optimizer
Adam
Batch size
Dynamics Randomization
Mini Batches
Friction
T((022 1.2)
Learning epoches
PD gain
24(0.9 1.1)
Entropy coefficient
0.01
Link mass(kg)
24(0.9, x default
Value loss coefficient
1.0
Ankle inertia(kg.m²)
4(0.9, x.1) default
Clip param Max grad norm
0.2
Buse CoM oflise((m)
U( 0.05, 0.05) 0.05x torque limit u(0, 40)
1.0
ERFI (N-m/kg)
Init noise std
0.8
Control delay(ms)
Learning
le-3
Desired
0.01
External Perturbation
GAE decay factor(
Random push interval(s) Random push velocity(m/s)
[5, 10] 0.1
GAE discount factor(r))
0.99
Actor ML.
[512, 256, 128]
Critic MLP size
[768, 512, 128]
MLP Activation
ELU
C.5 Curriculum Learning
To imitate nigh-dynamic motions, introduce two curriculum mechanisms: a termination curriculum that gradually reduces tracking error tolerance, and a penalty curriculum that progressively increases the weight of regularization terms, promoting more stable and physically plausible behaviors.
Termination Curriculum: The episode terminated early when the humanoid's 's motion deviates from the reference beyond termination threshold 0. During training, this threshold is gradually decreased increase the difficulty:
+- clip (0 (1 - 6), Oann, Omax).
(19)
where the initial threshold 2.5 10-5
1.5, with bounds 6mnn 0.3, 9max and decay rate ō
Pemalty Curriculum: To facilitate learning in the carly training stages while gradually enforcing stronger regularization, we introduce scaling factor that increases progressively to modulate the influence of the penalty term:
a clip (ax (1 6), Cmmin; (mmxx), Ppenalty f- a Tppenalt::
(20)
where the initial penalty scale a = 0.1, with bounds Ormin = 0.0, Qmax 1.0, and growth rate 8 1.0 x 10"
C.6 PD Controller Parameter
The gains of the PD controller are listed in Table 9 simulator in training, we manually set the inertia of the ankle links to a fixed value of x 10-3
To improve the numerical stability and fidelity of the
Table 9: PD controller gains.
Joint name
Stiffness (kpp)
Damping (kag)
Lettright shoulder pitch/roll/yaw
100
2.0
Lett/rght shoulder yaw
50
2.0
Lefvrrght elbow
50
2.0
Waist pitch/rollyyww
400
5.0
Left/rihtt hip pitch/roll/yaw
100
2.0
LefVright
4.0
LetVright ankle pitch/roll
2.0

---

D Experimental Details
D.1 Experiment Setup
Compute platform: Each experiment is conducted on machine with 24-core Intel i7-13700 CPU running at 5.2GHz, 32 GB of RAM, and single NVIDIA GeForce RTX 4090 GPU, with Ubuntu 20.04. Each of our models is trained for 27 hours.
We deploy our policies on Unitree G1 robot. The system consists of an onboard motion control board and external PC, connected via Ethernet. The control board collects sensor data and transmits it the PC using the DDS protocol. The PC maintains observation history, performs policy inference, and sends target joint angles back to the control board, which then issues motor commands.
Real robot setup:
D.2 Evaluation Metrics
Global Mcan Per Body Position Error (Eg mpbpe. mm): The average position error of body parts in global coordinates.
Egmmpppee E
Pi ref
(21)
Goot-Relative Mean Body Position Error (Emphpe, mm): The average position error body parts relative to the root position.
Emphpe
||| (p= Proot,s)
- (pi ref Proot,
(22)
Mean Joint Position Error (Fmppipe 10-3 rad); The average angular error of joint rotations.
Empipe
|
(23)
Mean Per Joint Velocity Error (Empjves rad/frame): The average error joint angular velocities.
Empjve E |1
Aq.
(24)
where Ag: q:
9t-1-
Mean Per Body Velocity Error (Emphve, mm/frame): The average emorr of body part linear velocities.
Empbve = E [p. Ap. App
where Ap. = P: P2-1.
Mean Per Body Acceleration Error (Fmpbaae mm/frame"): The average error of body part accelerations,
Emppac
A| A -2p
(26)
where A²p: Ap: Ap:-1-
D.3 Baseline Implementations
To ensure fair comparison, haseline methods are trained separately for each motion. We consider the following baselines:
OmniHH20: Omnil100 adopts teacher-student training paradigm. We moderately increase the
tracking reward weights better match the robot. In setup, the teacher and student policies are trained for 20 and 10 hours, respectively.
Exbody2: ExBody2 utilizes decoupled keypoint- tracking mechanism. The teacher and student policies are trained for 20 and 10 hours, respectively.
MaskedMimic: MaskedMimic comprises three sequential training phases and we utilize only first phase, as the remaining stages are not pertinent to our tasks. The method focuses on reproducing reference motions by directly optimizing pose-level accuracy, without explicit regularization of physical plausibility. Each policy is trained for 18 hours.
25

---

D.4
Tracking Factor Configurations
We define five sets of tracking factors: Coarse, Medium, UpperBound, LowerBound, and the initial values of Ours, as shown in Table I0 We also provide the converged tracking factors of our adaptive mechanism Table
Table 10: Tracking factors in different configurations.
Factor term
Ours(Init)
Coarse
Medium
Upperbound
Lowerbound
Joint position
0.3
0.3
0.08
0.02
Joint velocity
30.0
30.0
10.0
5.0
2.5
Body position
0.015
0.015
0.005
0.002
0.0003
Body rotation
0.1
0.1
0.03
0.4
0.02
Body velocity
1.0
1.0
0,3
0.12
0.03
Body angular velocity
15.0
15.0
5.0
3.0
1.5
Body position VRpoints
0.015
0.015
0.005
0.003
0.0003
Body position feet
0.01
0.01
0.003
0.003
0.0002
Max joint position
1.0
1.0
0.3
0.5
0.25
Table 11: Converged tracking factors of our adaptive mechanism across different motions in the
ablation study of Section 5.4
Factor term
Jabs punch
Charleston dance
Bruce Lee's pose
Roundhouse kick
Joint position
0.0310 0.0002
0.0360 + 0.0016
0.0268 0.0009
0.0261
0.0005
Joint velocity
2.8505 0.0419
5.5965 + 0.1797
3.6053 0.0323
4.3859
0.0537
Body position
0.0007 0.0000
0.0023 + 0.0001
0.0025
0.0000
0.0010 = 0.0000
Body rotation
0.0998 0,0000
0.0544 1 0.0016
0.0046 0.0001
0.0829 - 0.0176
Body velocity
0.0554 + 0.0006
0.0941 + 0.0013
0.0768 0.0001
0.0929 = 0.0008
Body angular velocity
1.8063 + 0.0076
2.8267 + 0.0841
2.17
0.0050
3.0238 = 0.0303
Body position VRpoints
0.0008 + 0,0000
0,0031 + 0.0002
0.0024
0.0000
0.0015 = 0.0000
Body position feet
0.0006 + 0.0000
0.0031 + 0.0001
0.0028
0.0000
0.0011 = 0.0000
Max joint position
0.3963 1 0.0003
0.4339 1 0.0124
0.3299 0.0064
0.3352 0.0010
E Additional Experimental Results
E.1 Analysis of Contact Mask Estimation and Motion Correction Method
Accuncy (84)
40
20
Height
Velecity
Ours
Figure 10: Accuracy of contact mask estimation across different methods.
Fig. 10 illustrates the accuracy of the proposed contact mask estimation method, evaluated on manually labeled motion dataset with samples. The proposed approach demonstrates an impressive accuracy 91 91.4%.
Fig. presents visual comparison of the efficacy the proposed motion correction technique mitigating floating artifacts, Prior to motion correction, the overall height of the SMPL model is noticeably elevated relative to the ground level. In contrast, after applying the correction, the model's motion aligns more accurately with the ground plane, effectively reducing the observed floating artifacts.
26

---

Before Correction
A
After Correction
Line aligned with ground level
Figure 11: Visualization of motion correction effectiveness in mitigating floating artifacts.
E.2
Ablation Study of Adaptive Motion Tracking Mechanism
Table 12
presents the ablation study results evaluating the impact of different tracking factors four motion tasks: Jabs Punch, Charleston Dance, Roundhouse Kick, and Bruce Lee's ' Pose.
Table 12: Ablation results of adaptive motion tracking mechanism in Section 5.4
Method
Epppppe
Empbpe
Empjpe
Emphve +
Empbac +
Empjye 4
Jahs punch
Ours
44.38
2.,53
18.736
5.52+a 156
6.23
88.01
Coarse
63.95-166600
36.7642.743
6.16:0011
6.46
91.46:10.46
Medium
51.07 +2,635
40.93
790.54
5.68 40.40
6.31 6.31 20,07
90.19+1.x21
Upperbound
45.74-11.700
28.72
793.52 28888
5.43
6.29 20.085
88.68 107777
Lowerbound
48.66.10.448
28.97 104487
781.73
5.61 5.6110009
6.31 10.026
88.44
Charleston dance
Ours
94.8 141..1
43.09 23.794
886.91 7:4.66
6.83 4:.3444334 346
2.25
162.70.g7.1338
Coarse
119.244.4550
15.80
1288 3.07
7.54 180
7.28
178.61
118.6113.300 334
Medium
83.63
41.02 1.773
933.33 1
6.89
10.185
7.22 7.22
10.011
164.92 144380
Upperbound
86.90&88.551 358.82
41.92 222632
917.64 14.85
7.02 100
7.22 000041
167.64 1:108
Lowerhound
145.42
I 1199.21
8.99
8.99
8.48
167.25
Roundhouse kick
Ours
$2.53
28.39
708.55 16.04
6.85 ::0 196
7.13
106.22
Coarse
76.81 1:2,863
38.98 222230
1008.32
1..34
1.00
108, 108.40
Medium
63. 12.12.43.178
33.74 4.2335
8006844.2 466.25
7.03 4.024
4.32
104.77 104.77
Upperbound
44.95442.164
31.31 3.434
766. 32
6.03
7.19=00012
105.64::1.911
Lowerbound
70.10.22.674
1..29
715.01
7.08
0.
102.50144650
Bruce Lee's pose
Ours
196.22-+17.08
69.12-42.399
972.04
7.57 +00214
8. 8.54
94.36++3.750
Coarse
239.06-451.74
80.78+15581
1678. 34 394.3
8.42++0.52
8.93
112.30++0.77
Medium
470.24
206.92
4490. 80
9.58
9.61=2.000
99.6 99.65
Upperhound
250.6441786
93.70=665.0
1358.
5
8.31
11.34
106.30
Lowerbound
158.1242.094
60.54_1..54
955.10 1
7.05
7.94
81.60
E.3 Ablation Study of Contact Mask
To evaluate the effectiveness of the contact mask, we additionally conducted an ablation study on three represen- tative motions characterized by distinct foot contact patterns: Charleston Dance, Jump Kick, and Roundhouse Kick. We additionally introduce the mean foot contact mask error metric:
Ecsntact-mask = [[|ce - 6
(27)
The results, shown in Table 13 demonstrate that method significantly reduces foot contact errors Erontact-maak compared to the baseline without the contact mask. In addition, it also leads to noticeable improvements other tracking metrics, validating effectiveness of proposed contact-aware design.
E.4
Additional Real-World Results
Fig. 12 presents additional results of deploying our policy the real world, covering more highly-dynamie motions. These results further validate the effectiveness of our method in tracking high dyyamii motions. enabling the humanoid to learn more expressive skills.
27

---

Table 13: Ablation results of contact mask.
Method
Prostact-mask
Emphpe +
Empjpe
Empbve +
Empbac +
Charleston dance
Ours
217.82 4777777
43.09
886.91 386.91124.76
7.26:2004
Ours w/o contact mask
633.911449.4
76.13113.00
980.40.222.0
7.72
10.51
Jump kick
Ours
294 620077
12.5848.126
840.33-497776
9.48
10.21 10.21
Ours w/o contact mask
686.75_.6006
479.28
1259
+,43.9
16.92
16.57 25.810
Roundhouse kick
Ours
243.16 1.776
28.39 1.440
708.55 16.04
6.85 1-01196
7.33 0:004
Ours w/o contact mask
250.10.66.23
36.76
921.52
6. 16.4000112
6, 6,46
Hookspunch
b) Horse-stance pose
Back kick
Side kick
e) Five stance form
f) Fighting combo
g) Tap dancé
Figure 12: Our robot masters more dynamic skills the real world. Time flows left to right.
Broader Impact
Our work advances humanoid robotics by enabling the imitation of complex, highly-dynamic human motions such as martial arts and dancing. This has broad potential in fields like physical assistance, rehabilitation, education, and entertainment, where expressive and agile robot behavior can support training, therapy, and interactive experiences. However, such capabilities also raise important ethical and societal concerns. High- agility robots interacting closely with humans introduce safety risks, and their potential to replace skilled human roles in performance, instruction, or service contexts may lead to labor displacement. Moreover, the misuse of advanced motion imitation for example, in surveillance concerns. These risks for clear regulation, strong safety mechanisms, and human oversight. Additionally, the environmental cost of training models and operating physical robots highlights the need for energy- and sustainable development. We believe this work should be viewed as step toward responsible, human-aligee aligned robotics, and we encourage continued dialogue on its socictal impact.
military applications poses security
28


Reviews:
[{"review_id": "c5DnXhXjdC", "reviewer": "Reviewer_oUB5", "summary": "The paper proposes \"filter - correct - retarget - reweight \" pipeline for realizing robust humanoid imitation of highly dynamic human motions like kungfu and dancing. The core innovation here is to (1) Define a stability metric inspired from zero moment point to filter our unstable motions. (2) Correct the motion to always have at least one foot contact with the actual ground and shift the motion accordingly. (3) Dynamically Reweight individual weights of the exponential kernel in the decomposed reward function to facilitate a natural curriculum for tracking individual joints more aggressively as the imitation behavior improves. They prove the efficacy of the approach by showcasing experimental results with sim2real transfer for a wide range of highly dynamic skills on G1 platform. Results show that the their method with adaptive nature of reward function and reward vectorization together allow them to outperform strong baslines like OmniH20 and Exbody2.", "questions": "*Questions*\n- I would love to know some thoughts from authors on the sim2real gap on G1. do you think the DR range suggested by the paper is enough and there is no sim2real gap ? What would you make out of papers like ASAP[1] which specifically deals with the sim2real gap of the ankle. \n\n\n[1] He, Tairan et al. “ASAP: Aligning Simulation and Real-World Physics for Learning Agile Humanoid Whole-Body Skills.” ArXiv abs/2502.01143 (2025): n. pag.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "*Strengths*\n- The filter-correct-retarget-reweight paradigm is highly practical and well motivated. The authors clearly showcase that the dynamics based filtering is an efficient proxy to filter out \"unrealizable\" motions. \n- The reweighting of individual reward components being paired with reward vectorization is very intuitive and well motivated. Ablation studies experimentally show that the adaptive reward tracking helps in overall performance especially in highly dynamic motions. \n- The final output of the controller in sim and especially real world on highly dynamic motions are very impressive. \n- The implementation details and other hyper-parameters are very detailed suggesting high chances of reproducibility.\n\n\n*Weakness*\n- No ablation study on reward vectorization. How crucial is the vectorization of rewards to make the adaptive reward mechanism to show benefits. \n- It would be interesting to see how masked-mimic performs if the regularizations were added and privileged information removed ? Or we can remove the regularizations from the proposed method as well - as an ablation study. Just shrugging masked-mimic off as a oracle-style lower bound while being a good anchor does not provide us much information of how much performance do we lose to each of the regularization components and privileged informations. \n- It would be interesting to further look into why the \"unrealizable\" motions are so. Did it happen due to pose tracking error from the video / Mocap data? In this context what kind of human motions even when perfectly tracked might be flagged as \"unrealizable\" ? Some discussion on this is very welcome.", "was_revised": true, "final_justification": "I am inclined to accept as training dynamic motions for humanoids is overall a brewing research topic and the paper showcases evidence that their training methodology provides a meaningful improvement on being able to train policies for a non-perfect diverse and dynamic dataset.", "rebuttal": "We sincerely thank the reviewer for their thoughtful and constructive feedback. We are glad that the reviewer found our proposed pipeline practical, well-motivated, and effective in enabling robust humanoid imitation of highly dynamic motions. We appreciate the positive comments on our real-world results, reward adaptation mechanism, and detailed implementation. We address the concerns raised point-by-point below.\n\n# W1: No ablation study on reward vectorization\n\nWe conducted ablation studies comparing performance with and without reward vectorization on representative motions, each with 3 seeds. The results across different training steps are summarized below. Overall, reward vectorization facilitates training and consistently improves early learning performance, especially noticeable in the first 10K steps.\n\n\n\n| Motion           | Setting  | Metric              | 5K                | 10K               | 30K               | 50K               |\n|------------------|----------|---------------------|-------------------|-------------------|-------------------|-------------------|\n| Jabs punch       | w/ RV   | Mean episode length      | 193.33 $\\pm$ 1.04      | 229.53 $\\pm$ 0.81      | 233.20 $\\pm$ 0.40      | 234.97 $\\pm$ 0.42      |\n|                  |          | Mean reward         | 8.02 $\\pm$ 0.07        | 13.81 $\\pm$ 0.49       | 14.41 $\\pm$ 0.08       | 15.84 $\\pm$ 0.38       |\n|                  | w/o RV    | Mean episode length      |  173.93 $\\pm$ 9.06             |  228.87 $\\pm$ 0.85             | 232.43 $\\pm$ 0.49             | 234.07 $\\pm$ 0.37            |\n|                  |          | Mean reward         | 7.05 $\\pm$ 0.51             |  13.06 $\\pm$ 0.50             | 14.26 $\\pm$ 0.10            | 15.75 $\\pm$ 0.37             |\n| Tai Chi          | w/ RV   | Mean episode length      | 169.67 $\\pm$ 0.37      | 253.90 $\\pm$ 1.76      | 358.83 $\\pm$ 4.07      | 375.03 $\\pm$ 1.33      |\n|                  |          | Mean reward         | 6.93 $\\pm$ 0.41        | 9.89 $\\pm$ 0.58        | 19.46 $\\pm$ 1.35       | 22.19 $\\pm$ 0.58       |\n|                  | w/o RV    | Mean episode length      | 167.27 $\\pm$ 1.42             | 254.43 $\\pm$ 3.21             | 354.43 $\\pm$ 0.77             | 372.87 $\\pm$ 1.41             |\n|                  |          | Mean reward         |6.59 $\\pm$ 0.44            | 10.29 $\\pm$ 0.37             | 19.01 $\\pm$ 0.53            | 22.07 $\\pm$ 0.30             |\n| Roundhouse kick  | w/ RV   | Mean episode length      | 96.62 $\\pm$ 7.75       | 120.50 $\\pm$ 1.66      | 125.73 $\\pm$ 0.07      | 127.37 $\\pm$ 0.32      |\n|                  |          | Mean reward         | 3.82 $\\pm$ 0.07        | 4.41 $\\pm$ 0.26        | 6.26 $\\pm$ 0.05        | 6.53 $\\pm$ 0.08        |\n|                  | w/o RV    | Mean episode length      | 97.34 $\\pm$ 2.06             |118.63 $\\pm$ 0.41             | 124.83 $\\pm$ 0.41            | 125.63 $\\pm$ 0.27             |\n|                  |          | Mean reward         | 3.85 $\\pm$ 0.48            | 4.40 $\\pm$ 0.25             | 6.15 $\\pm$ 0.05             | 6.46 $\\pm$ 0.36            |\n\n\n# W2: Loss from regularization and privilege information \n\nAs suggested, we conducted additional ablation experiments to enable a fairer comparison with MaskedMimic’s oracle setting. Specifically, we trained our method with privileged information and without domain randomization, which we refer to as *Ours (Oracle)*. The results are presented in the table below. \n\nIt demonstrates that our method achieves competitive or superior performance to MaskedMimic under identical oracle settings. \n\n    \n|  Level   | Method         | $E_{g-mpbpe}↓$    | $E_{mpbpe}↓$      | $E_{mpjpe}↓$       | $E_{mpbve}↓$     | $E_{mpbae}↓$     | $E_{mpjve}↓$       |\n| --- | -------------- | ---------------- | ---------------- | ----------------- | --------------- | --------------- | ----------------- |\n|  Easy   | Ours           | 53.25 $\\pm$ 8.80 | 28.16 $\\pm$ 3.06 | 725.62 $\\pm$ 8.10 | 4.41 $\\pm$ 0.16 | 4.65 $\\pm$ 0.07 | 81.28 $\\pm$ 1.02  |\n|     | MaskedMimic （Oracle）   | 41.79 $\\pm$ 0.86 | 21.86 $\\pm$ 1.02 | 739.96 $\\pm$ 9.98 | 5.20 $\\pm$ 0.12 | 7.40 $\\pm$ 0.17 | 132.01 $\\pm$ 4.47 |\n|     | **Ours（Oracle）** |   45.02 $\\pm$ 3.38 | 22.95 $\\pm$ 7.61 | 710.30 $\\pm$ 8.33 | 4.63 $\\pm$ 0.79 | 4.89 $\\pm$ 0.48 | 73.44$\\pm$ 6.21 |\n|  Medium   | Ours           | 126.48 $\\pm$ 12.08 | 48.87 $\\pm$ 3.38  | 1043.30 $\\pm$ 46.67 | 6.62 $\\pm$ 0.18 | 7.19 $\\pm$ 0.11  | 105.30 $\\pm$ 2.66  |\n|     | MaskedMimic (Oracle）    | 150.92 $\\pm$ 59.65 | 61.69 $\\pm$ 20.58 | 934.25 $\\pm$ 69.35  | 8.16 $\\pm$ 0.88 | 10.01 $\\pm$ 0.39 | 176.84 $\\pm$ 11.68 |\n|     | **Ours（Oracle）** |       66.85 $\\pm$ 22.49 | 29.56 $\\pm$ 6.50 | 753.69 $\\pm$ 44.83 | 5.34 $\\pm$ 0.19 | 6.58 $\\pm$ 0.13 | 82.73 $\\pm$ 1.39 |\n|  Hard   | Ours           | 290.36 $\\pm$ 69.56 | 124.61 $\\pm$ 26.76 | 1326.60 $\\pm$ 189.43 | 11.93 $\\pm$ 1.31 | 12.36 $\\pm$ 1.20 | 135.05 $\\pm$ 8.18 |\n|     | MaskedMimic（Oracle）    | 47.74 $\\pm$ 1.38   | 27.25 $\\pm$ 0.80   | 829.02 $\\pm$ 7.70    | 8.33 $\\pm$ 0.09  | 10.60 $\\pm$ 0.21 | 146.90 $\\pm$ 6.64 |\n|     | **Ours（Oracle）** |        79.25 $\\pm$ 34.70 | 34.74 $\\pm$  11.30 | 734.90$\\pm$  77.95 | 7.04 $\\pm$  0.71 | 8.34 $\\pm$  0.57 | 93.79 $\\pm$  8.68 |\n\n\n\n\n# W3: Unrealizable motion\n\nWe identify two main sources of “unrealizable” motions:\n1. Tracking artifacts: Motions from video or mocap may contain artifacts (e.g., teleporting, ground penetration, floating feet) due to reconstruction errors, which violate physical constraints and hinder learning. Imperfect motion retargeting can further exacerbate these issues.\n2. Robot limitations: Even with perfect tracking, some motions are infeasible due to mechanical capacity limitations, such as high-speed action, excessive torque, or unstable contact transitions. (e.g., toe balancing in ballet or rapid one-leg spins).\n\n\n# Q1: Sim2real gap\nIn our experiments, while our DR strategy effectively cover a wide range of scenarios, sim2real gap still exists, particularly for motions that heavily rely on ankle and waist pitch/roll actuation. We suspect this is partly due to the parallel-joint mechanical design of these modules, which introduces structural discrepancies between simulation and hardware. We also observe that robot-specific factors, including manufacturing variation and wear, influence sim2real performance.\n\nWe view the ASAP paper as a valuable and complementary approach. Its delta action model effectively mitigates sim2real discrepancies—especially at the ankle—and could potentially improve success rates and tracking accuracy. However, our results show that even without such corrections, our method achieves strong sim2real performance across dynamic skills, suggesting that ASAP addresses an important but not exclusive aspect of the sim2real challenge.\n\n\n\nWe hope the additional explanations helped address your concern. We will include the suggested analysis and comparison in the revised manuscript. We are happy to answer further questions that you may have."}, {"review_id": "c5yJm0HvDn", "reviewer": "Reviewer_TKpF", "summary": "This paper proposes PBHC, a physics-based motion imitation framework for humanoid robots to imitate highly dynamic human motions such as Kungfu and dancing. The method includes a motion processing stage to extract, filter, correct, and retarget motions, and an adaptive imitation stage inspired by a bi-level optimization and using an asymmetric actor-critic architecture. The framework is validated through simulation and real-world experiments, including a series of visually compelling demonstrations on the Unitree G1 robot.", "questions": "Providing the training time and learning curves for some representative motions could be helpful to the readers.", "limitations": "Yes.", "rating": 6, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "The paper provides strong real-world validation, demonstrating stable and expressive behaviors of the Unitree G1 robot in complex motion tasks. The idea of adaptively adjusting the tracking weight sigma is intuitive and seems very helpful. \n\nMany implementation details are provided in the supplementary which is helpful to the community to learn sim-to-real. In addition, comprehensive ablation studies are performed.\n\nDynamically adjusting sigma is intuitive, but I have some concerns about the authors’ theoretical justification and claims.\n\nSimply put, achieving a higher reward through reward design does not necessarily indicate a better policy.\n\nReward maximization should be the objective of the policy learning process itself. If we try to maximize the reward by modifying the reward function design, we can always change certain configurations to increase the reward value, but that does not imply improved reinforcement learning performance.\nThe optimization proposed in this paper aims to find an appropriate sigma under various conditions to increase the absolute value of the reward. However, this reward maximization does not guarantee a better policy, because the agent learns from temporal-difference (TD) errors, not just from receiving higher scalar reward values.\nSpecifically, if one action is better than another, a good reward function should provide clear distinctions to facilitate learning, rather than simply assigning a large reward to an action.\n\nThe reliance on contact masks limits the range of tasks that can be performed. It is primarily suited for foot-ground locomotion. Other agile motions such as climbing or rolling may become difficult or infeasible under current pipeline.", "was_revised": true, "final_justification": "The authors have addressed my concerns. I change the rating to 6: strong accept.", "rebuttal": "We sincerely thank the reviewer for their thoughtful and constructive feedback. We are encouraged that the reviewer found our real-world validation strong, the dynamic tracking weight adjustment intuitive, and appreciated our detailed implementation and ablation studies. We address your concerns point by point below::\n\n# W1: Reward maximization != good policy\n\nWe agree with your observation: simply increasing scalar reward values via reward shaping does not necessarily lead to a better policy, as policy learning is driven by TD errors and relative action advantages.\n\nHowever, we would like to clarify a possible misunderstanding of our formulation. Our method does not attempt to achieve a higher scalar reward by simply adjusting sigma. Rather, in our theoretical formulation (Sec.3.2.2), we model both the RL training and reward shaping into a bi-level optimization problem where: \n- The lower-level optimization, expressed as a simplified motion tracking problem, corresponds to the standard RL process, aiming to train a policy that maximizes the *fixed* tracking reward and other reward terms, given a specific sigma.\n- The upper-level optimization, which is not part of the RL loop, seeks the optimal sigma that minimizes the accumulated tracking error of the final converged policy. This outer optimization is *not reward maximization* but a performance-driven objective based on *absolute* external metrics.\n\nIn short, sigma is chosen not to maximize reward per se, but to guide the RL process such that the resulting policy achieves better *external performance*. \n\nIn the implementation, we integrate these two levels into a single-stage RL training process with a practical adaptive mechanism (Sec.3.2.3).\n\n\n# W2: Reliance on contact mask\n\nWe agree that our current framework is best suited for motions involving foot-ground contact, and this is a limitation for tasks such as climbing or rolling. However, the contact mask formulation is inherently generalizable. In principle, the same technique can be extended to detect and handle contacts for other body parts (e.g., hands, pelvis, head). We believe this simple yet general technique holds promise for enabling the imitation of a broader range of contact-rich behaviors.\n\n\n# Q1: Learning curve and training time\n\nThank you for the suggestion. We have provided training curves and wall-clock training times for representative motions in the following tables.\n\n*Training Time*: Aggregated across all main experiments since it's motion-agnostic.\n\n|  Iterations | 10K       | 20K       | 30K       | 40K| 50K       |\n|----------------------|-----------|-----------|-----------|----------|-----------|\n| Training Time (hours)| 5.38$\\pm$ 0.03 | 10.70$\\pm$ 0.11 | 15.97$\\pm$ 0.22|21.25 $\\pm$ 0.30|26.28 $\\pm$ 0.54|\n\n*Learning curve of typical motions*: Each row summarizes mean $\\pm$ standard error over 3 seeds.\n|  Motion  |  Metric  | 5K       | 10K       | 30K       | 50K       |\n|----------------------|----------------------|-----------|-----------|-----------|----------|\n|Jabs punch| Mean episode length| 193.33 $\\pm$ 1.04 |  229.53 $\\pm$ 0.81 |233.20 $\\pm$ 0.40|234.97 $\\pm$ 0.42|\n| | Mean reward| 8.02 $\\pm$ 0.07 | 13.81 $\\pm$ 0.49 |  14.41 $\\pm$ 0.08|15.84 $\\pm$ 0.38|\n| Tai Chi| Mean episode length| 169.67 $\\pm$ 0.37 | 253.90 $\\pm$ 1.76 | 358.83 $\\pm$ 4.07|375.03 $\\pm$ 1.33|\n| | Mean reward| 6.93 $\\pm$ 0.41 | 9.89 $\\pm$ 0.58 | 19.46 $\\pm$ 1.35|22.19 $\\pm$ 0.58|\n| Roundhouse kick| Mean episode length| 96.62 $\\pm$ 7.75 | 120.50 $\\pm$ 1.66 | 125.73 $\\pm$ 0.07|127.37 $\\pm$ 0.32|\n| | Mean reward| 3.82 $\\pm$ 0.07 | 4.41 $\\pm$ 0.26 | 6.26 $\\pm$ 0.05|6.53 $\\pm$ 0.08|\n\nWe hope this addresses your concerns. We will revise the paper to clarify our formulation, and include the requested training analysis. Let us know if there is any other clarification we can provide."}, {"review_id": "mXncJqxGRj", "reviewer": "Reviewer_qDky", "summary": "The paper studies the task of humanoid robotic imitation of full-body human motions. The authors first extract feasible motions from videos by combining prior approaches: they estimates candidate motions via GVHMR, then filter these motions based on the maximum distance between center of mass and center of pressure, apply a vertical correction, and then retarget motions to respect the joint limits of the G1 robot.\n\nNext, they train policies in simulation (including domain randomization) to track these motions via RL. To do this, they use an exponential tracking reward, whose distance parameter sigma is adaptively reduced over time, providing coarse shaping at the beginning and more precise shaping as training progresses. The trained policies are evaluated in simulation against the prior methods OmniH2O and ExBody2, demonstrating substantial improvement.\n\nFinally, policies are deployed on a real robot, demonstrating similar tracking performance as in simulation.", "questions": "1) Table 1 reports mean +/- one standard deviation. Presumably the goal is to identify which methods are significantly better than others; why not compute standard errors, and use them to report 95% CIs? (Or, if the data may not be normally distributed, you could report asymmetric CIs based on a nonparametric test, e.g. a bootstrap test.)\n\nBolding is currently done based on standard deviation of the best result, but this will underestimate errors; differences should be checked for significance using a test for difference in means, e.g. a t-test (or for non-normal data, a permutation test: https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.permutation_test.html).\n\n2) Could you provide some additional intuition for the derivation of optimal tracking sigma? I understand why shrinking sigma is useful in training (to provide successively finer reward shaping), but for the theoretical derivation it sounds like you care about the converged policy (153); why isn’t sigma for the optimal policy arbitrarily large, so that it’s as close to linear as possible, thus best mimicking the true linear tracking error J^ex?", "limitations": "Yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1) The adaptive motion tracking optimization is an elegant, theoretically-motivated solution to the reward shaping problem, a common problem in robotics. As shown in Figure 7, it avoids the need for task-specific tuning of tracking factor.\n2) Evaluations demonstrate clear improvements over prior recent work (Table 1).\n3) The full pipeline leads to impressive, highly dynamic motions achieved on the real robot, as shown in the supplementary videos.\n4) The paper is clearly written overall.\n\n**Weaknesses:**\n1) Separate policies are trained for each motion, limiting generalization (acknowledged by authors in limitations).\n2) Some of the statistical analysis seems nonstandard; see questions.", "was_revised": true, "final_justification": "In the rebuttal discussion, the authors added CIs and statistical significance calculations, resolving my concerns here. They also added ablations as suggested by reviewer oUB5, and provided additional explanation for their theoretical results.\n\nThe limitation of separate policies for each motion remains unresolved, but this is a limitation acknowledged by the authors, and I believe the paper remains strong despite this.\n\nI've read the review by reviewer 339U (who gave the lowest score), but the author's responses seem to address the concrete concerns, and I believe the paper's value rests on its strong empirical results for their simple and elegant method.", "rebuttal": "We thank Reviewer qDky for the detailed and insightful feedback. We appreciate your recognition of the theoretical contribution, real-world results, and clarity of presentation. Below, we respond to your questions and concerns:\n\n\n# W1: Limited to single motion\n\nWe thank the reviewer for highlighting this important limitation. While our current framework trains separate policies per motion, it can be naturally extended to multi-motion settings by incorporating reference motion states as inputs and modestly expanding the network architecture. We view this as a valuable direction for future work.\n\n# Q1: Statistical significance\n\nWe have revised the Table 1 to report mean $\\pm$ standard error (instead of standard deviation)  and include statistical significance testing between our methods and each baseline method. Specifically, we conducted two-sided permutation tests (as recommended) to assess whether the observed differences in means are statistically significant.\n\nSignificant improvements (p < 0.05) by *Ours* over baselines are marked with asterisks (\\*) in the table for clarity. The additional results of *Ours(Oracle)*, suggested by other reviewers, are also reported to compare with *MaskedMimic(Oracle)*.\n\nAcross many metrics and difficulty levels, *Ours* shows statistically significant improvements over prior methods, confirming the robustness of our approach.\n\n| Level    | Method         | $E_{g-mpbpe}↓$      | $E_{mpbpe}↓$        | $E_{mpjpe}↓$          | $E_{mpbve}↓$       | $E_{mpbae}↓$      | $E_{mpjve}↓$        |\n| --- | -------------- | ------------------ | ------------------ | -------------------- | ----------------- | ---------------- | ------------------ |\n| Easy    | OmniH2O        | 233.54 $\\pm$ 2.00* | 103.67 $\\pm$ 0.95* | 1805.10 $\\pm$ 6.15*  | 8.54 $\\pm$ 0.06*  | 8.46 $\\pm$ 0.04* | 224.70 $\\pm$ 1.02  |\n|     | Exbody2        | 588.22 $\\pm$ 5.71* | 332.50 $\\pm$ 1.79* | 4014.40 $\\pm$ 10.75* | 14.29 $\\pm$ 0.08* | 9.80 $\\pm$ 0.07* | 206.01 $\\pm$ 0.67* |\n|     | Ours           | 53.25 $\\pm$ 8.80   | 28.16 $\\pm$ 3.06   | 725.62 $\\pm$ 8.10    | 4.41 $\\pm$ 0.16   | 4.65 $\\pm$ 0.07  | 81.28 $\\pm$ 1.02   |\n|     | MaskedMimic（Oracle）    | 41.79 $\\pm$ 0.86   | 21.86 $\\pm$ 1.02   | 739.96 $\\pm$ 9.98*    | 5.20 $\\pm$ 0.12   | 7.40 $\\pm$ 0.17*  | 132.01 $\\pm$ 4.47*  |\n|     | Ours（Oracle） |   45.02 $\\pm$ 3.38 | 22.95 $\\pm$ 7.61 | 710.30 $\\pm$ 8.33 | 4.63 $\\pm$ 0.79 | 4.89 $\\pm$ 0.48 | 73.44$\\pm$ 6.21 |\n| Medium    | OmniH2O        | 433.64 $\\pm$ 7.25*  | 151.42 $\\pm$ 3.28* | 2333.90 $\\pm$ 22.14* | 10.85 $\\pm$ 0.13  | 10.54 $\\pm$ 0.07 | 204.36 $\\pm$ 2.00  |\n|     | Exbody2        | 619.84 $\\pm$ 11.70* | 261.01 $\\pm$ 0.71* | 3738.70 $\\pm$ 12.04* | 14.48 $\\pm$ 0.07* | 11.25 $\\pm$ 0.08 | 204.33 $\\pm$ 0.97* |\n|     | Ours           | 126.48 $\\pm$ 12.08  | 48.87 $\\pm$ 3.38   | 1043.30 $\\pm$ 46.67  | 6.62 $\\pm$ 0.18   | 7.19 $\\pm$ 0.11  | 105.30 $\\pm$ 2.66  |\n|     | MaskedMimic（Oracle）    | 150.92 $\\pm$ 59.65 * | 61.69 $\\pm$ 20.58 * | 934.25 $\\pm$ 69.35 *  | 8.16 $\\pm$ 0.88*   | 10.01 $\\pm$ 0.39* | 176.84 $\\pm$ 11.68* |\n|     | Ours（Oracle） |       66.85 $\\pm$ 22.49 | 29.56 $\\pm$ 6.50 | 753.69 $\\pm$ 44.83 | 5.34 $\\pm$ 0.19 | 6.58 $\\pm$ 0.13 | 82.73 $\\pm$ 1.39 |\n|   Hard  | OmniH2O        | 446.17 $\\pm$ 6.42  | 147.88 $\\pm$ 2.07  | 1939.50 $\\pm$ 11.94  | 14.98 $\\pm$ 0.32 | 14.40 $\\pm$ 0.29 | 190.13 $\\pm$ 4.10  |\n|     | Exbody2        | 689.68 $\\pm$ 5.90  | 246.40 $\\pm$ 0.62* | 4037.40 $\\pm$ 8.37*  | 19.90 $\\pm$ 0.10 | 16.72 $\\pm$ 0.08 | 254.76 $\\pm$ 1.70* |\n|     | Ours           | 290.36 $\\pm$ 69.56 | 124.61 $\\pm$ 26.76 | 1326.60 $\\pm$ 189.43 | 11.93 $\\pm$ 1.31 | 12.36 $\\pm$ 1.20 | 135.05 $\\pm$ 8.18  |\n|     | MaskedMimic（Oracle）    | 47.74 $\\pm$ 1.38   | 27.25 $\\pm$ 0.80   | 829.02 $\\pm$ 7.70*    | 8.33 $\\pm$ 0.09 * | 10.60 $\\pm$ 0.21* | 146.90 $\\pm$ 6.64*  |\n|     | Ours（Oracle） |        79.25 $\\pm$ 34.70 | 34.74 $\\pm$  11.30 | 734.90$\\pm$  77.95 | 7.04 $\\pm$  0.71 | 8.34 $\\pm$  0.57 | 93.79 $\\pm$  8.68 |\n\n\n\n\n# Q2: Intuition of theoretical derivation \n\n> Why you are shrinking sigma in training time but talking about the converged policy for theoretical derivation?\n\nIn short, our strategy of shrinking sigma during training is for approximately solving the theoretical formulation.\n\nIn our theoretical derivation, we do care about the converged policy, and consider the problem as a bi-level optimization, where the lower level corresponding to RL training and the upper level corresponding to reward tuning. Meanwhile, in the implementation, we integrate these two levels into a single-stage RL training process with a practical adaptive mechanism (Sec.3.2.3). \n\nThis integration is for practical considerations. While accessing to the precise performance of a specific sigma requires a converged policy, and iteratively train multiple policies to explore the suitable sigma is expensive, we use the EMA of tracking error during training to roughly access the converged performance. This provides a tractable and gradually accurate signal for adjusting sigma. As training proceeds and the policy converges, this approximation becomes increasingly reliable. Hence the converged policy trained with adaptive module should reflect the theoretical optimal solution. \n\n> Why isn’t sigma for the optimal policy arbitrarily large?\n\nWhile a larger sigma makes the $J^{in}$ mimicking the linear objective $J^{ex}$, this does not imply that the converged policy from the inner RL optimization will minimize $J^{ex}$. The bi-level formulation explicitly models this distinction.\n\nFrom a theoretical perspective, the lower level problem is subject to complex factors, including environment dynamics and implicit regularization, modelled by $R(x)$. These factors will bias the solution and prevent the learned policy from exactly minimizing $J^{ex}$. The upper level problem chooses sigma to improve the actual tracking outcome—not to match the functional form of the reward.\n\nFrom a practical perspective, setting sigma too large makes the reward too flat, weakening the learning signal. This makes the RL agent focus more on other rewards and leads to training failure. This is aligned with the above theoretical analysis.\n\n\n\nThank you again for the thoughtful feedback and for recognizing the contributions of this work. If there are any questions you would like to discuss, please let us know."}, {"review_id": "HHPC2xNISC", "reviewer": "Reviewer_339U", "summary": "The paper introduces KungfuBot, a framework for learning highly dynamic whole-body humanoid control using reinforcement learning. It tackles the limitations of prior approaches that struggle with fast, agile motions by combining a multi-stage physics-based motion processing pipeline with an adaptive motion tracking mechanism. The system extracts human motions from video, filters them using physical feasibility criteria, corrects artifacts, and retargets them to a humanoid robot. A novel bi-level optimization formulation dynamically adjusts tracking precision during training, enabling better reward shaping. The policy is trained using an asymmetric actor-critic RL architecture and successfully deployed zero-shot on the Unitree G1 robot, demonstrating expressive skills such as Kungfu and dancing. The method significantly outperforms existing baselines in both simulation and real-world evaluations.", "questions": "Please address the weaknesses raised above.", "limitations": "Yes.", "rating": 3, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n- The proposed method enables a humanoid robot to learn and execute agile and complex motions (e.g., Kungfu, dance), outperforming prior work in tracking precision and expressiveness.\n- The pipeline uses physical plausibility metrics (CoM-CoP stability) to filter out untrackable motions, increasing training efficiency and real-world robustness.\n- The introduction of a principled, adaptive reward shaping mechanism that dynamically tunes tracking precision is both novel and practically impactful, helping generalize across motions of varying difficulty.\n- The real-world experiments look strong and convincing.\n\n\n**Weaknesses**\n- It might not be justified to compare the method with ASAP on the number of stages if each stage of the proposed method involves multiple steps. Additionally, the MoCap component in ASAP is used to propose delta actions as real-time compensations, which deal with a topic that the paper does not cover.\n- In motion filtering, it is not clear how the correct thresholds for stability, velocity and height are selected. Experiment 5.2 justifies the selection with policies trained on each of the motions. However, considering the inherent difficulty within the motions, some of the learnable but hard ones are filtered out depending on these base policies.\n- If motion filtering is presented as a contribution of the paper, it is worth considering discussions about other methods such as progressive training [1], learning-progress based automatic curriculum [2], physics-based retargetting [3].\n- How is the formulation of the adaptive tracking factor tuning related to a formulation based on a constrained MDP, where the objective is the accumulated negative tracking error and the constraint is the internal objective and the regularizations being larger than some threshold?\n- The approximation of the average optimal tracking error with the instantaneous tracking error is not reasonable, as it boils down to a simple curriculum where $\\sigma$ decreases (which tightens the distance) when $\\hat{x}$ goes down (error becomes smaller). \n- Each policy is trained for a specific motion. While the proposed adaptive tracking strategy demonstrates effectiveness, the paper fails to show a further generality to multiple motions. I would imagine the tracking factor would also vary across different motions in that case.\n- As each policy is trained for a specific motion and the selected baselines are focusing on multi-motion tracking, whose performance might be hindered due to this ambitious objective, it may make more sense to evaluate the proposed method against simple baselines on tracking single motions, such as DeepMimic.\n\n\n[1] Luo, Z., Cao, J., Kitani, K. and Xu, W., 2023. Perpetual humanoid control for real-time simulated avatars. In Proceedings of the IEEE/CVF International Conference on Computer Vision (pp. 10895-10904).\n\n[2] Li, C., Stanger-Jones, E., Heim, S. and Kim, S., 2024. Fld: Fourier latent dynamics for structured motion representation and learning. arXiv preprint arXiv:2402.13820.\n\n[3] Grandia, R., Farshidian, F., Knoop, E., Schumacher, C., Hutter, M. and Bächer, M., 2023. Doc: Differentiable optimal control for retargeting motions onto legged robots. ACM Transactions on Graphics (TOG), 42(4), pp.1-14.", "was_revised": true, "final_justification": "Most of my concerns have been addressed by the authors during the rebuttal phase. Given the work's limited improvement versus existing works and the missing details as pointed out, I will increase my score to borderline reject.", "rebuttal": "Thanks for the detailed and thoughtful feedback. We are encouraged that reviewer 339U appreciated our framework’s ability to learn expressive and agile humanoid skills and the strength of our real-world results. We address the raised concerns in detail below.\n\n    \n# W1: ASAP\nWe agree that comparing the number of training stages with ASAP was imprecise. We will revise the text to avoid this unfair comparison. Additionally, we acknowledge that ASAP’s delta action policy addresses sim-to-real compensation in a different way, which is beyond the scope of our method. We will clarify this distinction in the paper.\n\n# W2: Threshold selection in motion filter \n\nOur goal in motion filtering is not to establish an absolute notion of trackability, but rather to reliably distinguish clearly learnable motions from those that consistently fail under practical training settings. While some borderline cases might eventually succeed with more sophisticated methods, our thresholds serve the practical goal of enabling robust policy training at scale.\n\nWe selected the filtering thresholds based on small-scale preliminary experiments and then validated them on a larger set. To further justify the selected parameters, we provide ablations below. Each table sweeps one parameter with others fixed to default (asterisk, \\*) values. The results support the effectiveness of our chosen thresholds.\n\nFor the motion filtering thresholds, we report the F1 score $F_1= \\frac{2*\\text{Precision}\\cdot{\\text{Recall}}}{\\text{Precision}+{\\text{Recall}}}$ of classifying motions as trackable (Episode Length Ratio > 60%) on the same dataset as in Section 5.2, where $\\epsilon_{\\mathrm{stab}}$ defines the maximum CoM–CoP distance for a frame to be considered stable, and $\\epsilon_N$ sets the maximum length of consecutive unstable frames allowed in a motion. \n\n| $\\epsilon_{stab}$ | 0.01   | 0.05   | 0.1\\* | 0.2    | 0.5  |\n|:---------------:|--------|--------|-----|--------|-----|\n|     F1 Score $↑$    | 0.5714 | 0.6154 | *1*\\*   | 0.6667 | 0    |\n\n| $\\epsilon_N$ | 10     | 50     | 100\\* | 150    | 200    |\n|:------------:|--------|--------|-----|--------|--------|\n|   F1 Score $↑$  | 0.6154 | 0.6154 | *1*\\*   | 0.8571 | 0.6667 |\n\n\n\nFor the thresholds used in contact mask estimation, we evaluate the accuracy of correctly detecting both feet’s contact states, where the contact state of one feet is estimated according to $c_t=\\mathbb{I}[\\|\\|p_{t+1}-p_t \\|\\|^2_2<\\epsilon_{vel}]\\cdot \\mathbb{I}[ p_{t,z}<\\epsilon_{height} ]$. The results are obtained from the same dataset as Appendix E.1 (Fig 9).\n\n\n| $\\epsilon_{vel}$ | 0.0001           | 0.001            | 0.002\\*            | 0.003            | 0.005            | 0.01             |\n|--------------|------------------|------------------|------------------|------------------|------------------|------------------|\n|        Acc(%)$↑$     | 77.42 $\\pm$ 8.65 | 90.82 $\\pm$ 4.51 | *91.40 $\\pm$ 5.10*\\* | 89.72 $\\pm$ 5.28 | 88.37 $\\pm$ 5.42 | 87.00 $\\pm$ 5.80 |\n\n| $\\epsilon_{height}$ | 0.01     | 0.1         | 0.15             | 0.2\\*              | 0.25             | 0.3              | 0.5              |\n|:-----------------:|------------------|-------------------|------------------|------------------|------------------|------------------|------------------|\n|        Acc(%)$↑$        | 7.59 $\\pm$ 15.19 | 11.21 $\\pm$ 16.31 | 81.33 $\\pm$ 9.41 | *91.40 $\\pm$ 5.10*\\* | 87.93 $\\pm$ 6.00 | 86.90 $\\pm$ 6.20 | 84.87 $\\pm$ 7.35 |\n\n\n# W3: Discussion about other motion filter methods\n\nThank you for the suggestion. We will add a discussion comparing our motion filtering with related approaches. Our method focuses on physically-plausible motion selection prior to training, aiming to reduce downstream learning difficulty. In contrast, progressive training and learning-progress curricula adaptively adjust training difficulty during learning. DOC retargets motions via differentiable optimization to obtain physically feasible motion, but has so far only succeeded on quadruped robots due to the complexity of humanoid dynamics.\n\n\n# W4: Formulation of adaptive tracking factor\n\nWhile we did not explicitly formulate our method as a constrained MDP, the goal is indeed related—both aim to optimize final policy performance under certain constraints. \n\nOur bi-level formulation separates concerns: the lower level corresponds a standard RL problem (MDP), while the upper level considers the tracking factor based on absolute policy performance. This separation makes our method compatible with off-the-shelf RL algorithms. \n\nA constrained MDP formulation could express similar objectives by integrating external and internal objectives. While the formulation is more unified, solving CMDPs in practice is more complex and often requires custom algorithms such as Lagrangian relaxation or dual ascent.\n\n\n\n# W5: Reasonability of adaptive curriculum\n\nWe approximate the average tracking error using an *exponential moving average* of the instantaneous error during training. EMA provides a smooth and relatively stable estimate of the current policy’s average tracking error, and it gradually approaches the optimal tracking error as the policy converges.\n\nAlthough the resulting update rule for sigma is simple in form, it is grounded in a principled formulation derived from our bi-level optimization. To our knowledge, ours is the first to provide a quantitative rule for determining sigma in motion tracking, supported by theoretical and empirical insights.\n\n\n# W6: Generality to multiple motions\n\nOur formulation can be naturally extended to the multi-motion setting by concatenating the error sequences from all motions into a single sequence. The rest of the derivation remains unchanged.\n\nWe acknowledge that different motions may have different optimal tracking factors. In multi-motion training, however, a unified tracking factor is typically required, as in prior works such as OmniH2O \\[1\\], Exbody2 \\[2\\] and GMT \\[3\\]. In such cases, our formulation has the potential to offer an advantage by adaptively estimating a shared tracking factor, which may outperform manually tuned fixed values.\n\nWe focused on single-motion training in this work to better study highly dynamic and expressive motions. Extending the method to multi-motion training is a promising direction that we believe deserves a dedicated investigation.\n\n\\[1\\] T. He _et al._, “OmniH2O: Universal and Dexterous Human-to-Humanoid Whole-Body Teleoperation and Learning,” Jun. 13, 2024, _arXiv_: arXiv:2406.08858.\n\n\\[2\\] M. Ji _et al._, “ExBody2: Advanced Expressive Humanoid Whole-Body Control,” Mar. 12, 2025, _arXiv_: arXiv:2412.13196. \n\n\\[3\\] Z. Chen _et al._, “GMT: General Motion Tracking for Humanoid Whole-Body Control,” Jun. 17, 2025, _arXiv_: arXiv:2506.14770.\n\n\n# W7: Baseline on single-motion tracking\n    \nWe clarify that all baselines, including OmniH2O and Exbody2, are trained individually for each motion, rather than using a multi-motion training setup, therefore ensures a fair comparison. Our MaskedMimic baseline in fact corresponds to the first-stage policy of the original paper only, which is equivalent to DeepMimic you mentioned.\n    \nAdditionally, we conducted additional ablation experiments to enable a fairer comparison with MaskedMimic’s oracle setting. Specifically, we trained our method with privileged information and without domain randomization, which we refer to as *Ours (Oracle)*. The results are presented in the table below. \n    \n    \nIt demonstrates that our method achieves competitive or superior performance to MaskedMimic under identical oracle settings. \n    \n|  Level   | Method         | $E_{g-mpbpe}↓$    | $E_{mpbpe}↓$      | $E_{mpjpe}↓$       | $E_{mpbve}↓$     | $E_{mpbae}↓$     | $E_{mpjve}↓$       |\n| --- | -------------- | ---------------- | ---------------- | ----------------- | --------------- | --------------- | ----------------- |\n|  Easy   | Ours           | 53.25 $\\pm$ 8.80 | 28.16 $\\pm$ 3.06 | 725.62 $\\pm$ 8.10 | 4.41 $\\pm$ 0.16 | 4.65 $\\pm$ 0.07 | 81.28 $\\pm$ 1.02  |\n|     | MaskedMimic （Oracle）   | 41.79 $\\pm$ 0.86 | 21.86 $\\pm$ 1.02 | 739.96 $\\pm$ 9.98 | 5.20 $\\pm$ 0.12 | 7.40 $\\pm$ 0.17 | 132.01 $\\pm$ 4.47 |\n|     | **Ours（Oracle）** |   45.02 $\\pm$ 3.38 | 22.95 $\\pm$ 7.61 | 710.30 $\\pm$ 8.33 | 4.63 $\\pm$ 0.79 | 4.89 $\\pm$ 0.48 | 73.44$\\pm$ 6.21 |\n|  Medium   | Ours           | 126.48 $\\pm$ 12.08 | 48.87 $\\pm$ 3.38  | 1043.30 $\\pm$ 46.67 | 6.62 $\\pm$ 0.18 | 7.19 $\\pm$ 0.11  | 105.30 $\\pm$ 2.66  |\n|     | MaskedMimic（Oracle）    | 150.92 $\\pm$ 59.65 | 61.69 $\\pm$ 20.58 | 934.25 $\\pm$ 69.35  | 8.16 $\\pm$ 0.88 | 10.01 $\\pm$ 0.39 | 176.84 $\\pm$ 11.68 |\n|     | **Ours（Oracle）** |       66.85 $\\pm$ 22.49 | 29.56 $\\pm$ 6.50 | 753.69 $\\pm$ 44.83 | 5.34 $\\pm$ 0.19 | 6.58 $\\pm$ 0.13 | 82.73 $\\pm$ 1.39 |\n|  Hard   | Ours           | 290.36 $\\pm$ 69.56 | 124.61 $\\pm$ 26.76 | 1326.60 $\\pm$ 189.43 | 11.93 $\\pm$ 1.31 | 12.36 $\\pm$ 1.20 | 135.05 $\\pm$ 8.18 |\n|     | MaskedMimic（Oracle）    | 47.74 $\\pm$ 1.38   | 27.25 $\\pm$ 0.80   | 829.02 $\\pm$ 7.70    | 8.33 $\\pm$ 0.09  | 10.60 $\\pm$ 0.21 | 146.90 $\\pm$ 6.64 |\n|     | **Ours（Oracle）** |        79.25 $\\pm$ 34.70 | 34.74 $\\pm$  11.30 | 734.90$\\pm$  77.95 | 7.04 $\\pm$  0.71 | 8.34 $\\pm$  0.57 | 93.79 $\\pm$  8.68 |   \n\n\nWe thank the reviewer again for the detailed, valuable feedback. We hope our responses have addressed all concerns, and we remain happy to answer any further questions."}]

Author rebuttal:

Meta-review: The paper proposes an approach for humanoid robots to imitate dynamic full-body human movement demonstrations. The proposed approach consists of a pipeline with a smart combination of existing techniques together with following the humanoid optimized motions using domain randomized reinforcement learning. For adapting to the desired motions gradually, the paper uses a reward schedule that forces the humanoid motions closer to the desired trajectory as the training progresses.

Strengths of the paper include a well thought out framework combining existing techniques with additional advances resulting in high performance humanoid motions, strong performance compared to baselines, real world robot experiments, and a well written paper. One potential weakness is that policies are not general but limited to each motion.

Overall, the paper provides a scientific advance in humanoid motion imitation and experimental evidence including demonstrations with a real robot.

During the rebuttal the authors provided stronger statistical support for the results, further comparisons and ablation studies. The rebuttal phase resulted in resolving most concerns.
Decision: Accept (poster)