Spherical Latent Motion Prior for Physics-Based Simulated Humanoid Control

Jing Tan; Weisheng Xu; Xiangrui Jiang; Jiaxi Zhang; Kun Yang; Kai Wu; Jiaqi Xiong; Shiting Chen

cs.ROMar 1, 2026

Spherical Latent Motion Prior for Physics-Based Simulated Humanoid Control

Authors: Jing Tan, Weisheng Xu, Xiangrui Jiang, Jiaxi Zhang, Kun Yang, Kai Wu, Jiaqi Xiong, Shiting Chen,

Organizations: The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China · University of Oxford, Oxford, United Kingdom

Abstract

Learning motion priors for physics-based humanoid control is an active research topic. Existing approaches mainly include variational autoencoders (VAE) and adversarial motion priors (AMP). VAE introduces information loss, and random latent sampling may sometimes produce invalid behaviors. AMP suffers from mode collapse and struggles to capture diverse motion skills. We present the Spherical Latent Motion Prior (SLMP), a two-stage method for learning motion priors. In the first stage, we train a high-quality motion tracking controller. In the second stage, we distill the tracking controller into a spherical latent space. A combination of distillation, a discriminator, and a discriminator-guided local semantic consistency constraint shapes a structured latent action space, allowing stable random sampling without information loss. To evaluate SLMP, we collect a two-hour human combat motion capture dataset and show that SLMP preserves fine motion detail without information loss, and random sampling yields semantically valid and stable behaviors. When applied to a two-agent physics-based combat task, SLMP produces human-like and physically plausible combat behaviors only using simple rule-based rewards. Furthermore, SLMP generalizes across different humanoid robot morphologies, demonstrating its transferability beyond a single simulated avatar.

Figures & tables

Figure 1: Overview of the Spherical Latent Motion Prior (SLMP). We collect a two-hour combat motion capture dataset and convert it into SMPL motion clips for training. We train a goal-conditioned motion tracking controller, then distill it into a unit-sphere latent space using three losses: imitation, discriminator, and our discriminator-guided local semantic consistency loss ( $L_{\text{DLSC}}$ ). SLMP supports meaningful random sampling and drives downstream tasks such as two-agent combat via simple rewards.

Figure 2: Qualitative examples of random latent-conditioned rollouts generated by SLMP. Uniformly sampled latent codes produce diverse, stable, and physically plausible full-body motions. Additional rollouts are provided in the supplemental video.

Figure 3: Latent-space motion tracking performance. We evaluate information loss by tracking reference clips through the latent space. SLMP achieves higher success and lower MPJPE than PULSE, and approaches the expert controller.

Figure 4: Qualitative comparison of random latent-conditioned rollouts. ASE exhibits repetitive low-diversity behaviors, PULSE collapses occasionally, and SLMP generates diverse and stable motions. See supplemental video for full rollouts.

Figure 5: Random latent rollout survival curves over 1000 trials in Isaac Gym. SLMP maintains substantially higher survival rates across long horizons, whereas PULSE survival degrades due to semantic sparsity in the tails of its VAE latent space.

Figure 6: State-dependent spherical latent manifold. left: a guard stance yields diverse feasible follow-ups with multiple regions on the sphere. right: an airborne kick yields only a few feasible continuations, causing the sphere to collapse into one or two regions.

Method	Success (%) $\uparrow$	MPJPE $\downarrow$	Survival(%) $\uparrow$
VAE	99.8	33.7	10.2
VQ-VAE	99.0	36.9	12.4
Sphere	100.0	31.5	0.1
SLMP (ours)	100.0	31.7	99.8

Table 1: Ablation over latent representations. Success rate and MPJPE measure latent tracking quality. Survival measures random rollout stability under uniform sampling, defined as the percentage of 1000 randomly sampled rollouts that do not result in a fall within 10 seconds.

Figure 7: Each row shows a rollout sampled from different latent structures.

Figure 8: Survival rate at 10 seconds under random latent sampling.

Figure 9: Each row shows a rollout sampled from the latent sphere under a different training loss configuration.

Figure 10: Qualitative results on the two-agent combat task using SLMP as a motion prior. We compare dense NCP-style rewards, Smplolympics-style rewards (NCP-style rewards augmented with AMP reward), and sparse rule-based rewards. NCP-style rewards lead to degenerate stationary interactions, while Smplolympics-style rewards bias the policy toward repetitive punching behaviors. In contrast, sparse rule-based rewards with SLMP produce diverse and human-like combat behaviors.

Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 11: Random latent sampling on realistic humanoid robot models in simulation. Top: Unitree G1. Bottom: ENGINEAI PM01. Both models can stably generate diverse motions under random latent inputs.

Figure 12: Two-agent combat evaluation on realistic humanoid robot models in simulation. Top: Unitree G1. Bottom: ENGINEAI PM01. The robots generate human-like combat behaviors under the SLMP prior.

Category	Action Types	Attributes & Targets	Clips	Dur.
Stance	Orthodox (Idle, Guard), Weight Shift	Speed: Slow, Normal	20	11s
Footwork	Step, Pivot ( $90^{\circ}$ ), Shuffle	Step Size: Small, Large	62	11s
Straight Punches	Jab, Cross	Target: Head, Body, Downward	60	11s
Hooks & Swings	Hook, Swing	Target: Head, Body; Type: Flat/Up	50	11s
Uppercuts	Uppercut (Left/Right)	Target: Head, Body	25	11s
Front Kicks	Front Kick (Left/Right)	Target: Body; Incl. Heavy Bagss	40	11s

Appendix

Table 2: Statistics of the combat motion capture dataset (502 clips). The dataset covers diverse speeds and target levels.

Component	Hidden Units	Activation
$\pi_{\text{track}}$	[2048, 1536, 1024, 1024, 512, 512]	SiLU
$E(\cdot)$	[512, 256]	ReLU
$\pi_{\varphi}$	[4096, 2048, 1024, 1024, 512, 512]	SiLU
$D(\cdot)$	[4096, 2048, 1024, 512]	ReLU
$\pi_{h_{1}},\pi_{h_{2}}$	[2048, 1024, 512]	SiLU

Appendix

Table 3: Network architectures used in our framework. All networks are implemented as multilayer perceptrons (MLPs).

PPO Hyperparameters
Batch Size	Env Num	LR	$\gamma$	Clip $\epsilon$
$32768$	$1024$	$5\times 10^{-5}$	$0.99$	$0.2$
SLMP Hyperparameters
$\lambda_{\text{distill}}$	$\lambda_{\text{disc}}$	Disc LR	$\lambda_{\text{DLSC}}$	$\beta$	$d$
$1.0$	$1\times 10^{-4}$	$5\times 10^{-5}$	$1.0$	$0.1$	$64$

Appendix

Table 4: Key hyperparameters used in our experiments.

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Learning Context-Aware Motion Priors for Humanoid Control

Yunyang Mo, Yi Gu, Yangchen Zhou, Hanyang Cao+1

The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China

RL for Robotics Robot Policy Learning Humanoid Robot Control

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Motion priors provide powerful guidance for learning naturalistic humanoid behaviors. However, existing methods typically learn a general, task-agnostic prior from the entire reference dataset and apply it uniformly throughout policy training. As a result, the prior cannot distinguish which reference motions are relevant to the current task context, potentially providing irrelevant or conflicting guidance. We present Context-Aware Motion Priors (CMP), a framework that adapts a general motion prior to the current task context without manual skill labels, dataset partitioning, or a separate skill discovery stage. Specifically, CMP learns context-motion compatibility using high-advantage policy rollouts, while a demonstration-based objective keeps the learned relevance grounded in the reference distribution. The resulting relevance scores reweight reference supervision for training a lightweight context-conditioned adapter. To evaluate the effectiveness and generality of CMP, we instantiate it with both Adversarial Motion Priors and Score-Matching Motion Priors. Across five humanoid control tasks, CMP consistently improves task performance and sample efficiency, learns meaningful context-motion alignment, and remains robust to imbalanced reference distributions. These results show that adapting motion priors to task contexts provides more relevant guidance for humanoid policy learning.

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