In the physical world we inhabit, space and time are fundamentally continuous. However, existing machine learning paradigms for world modeling are largely confined to discrete-time prediction, thereby exhibiting significant inefficiency in capturing the dynamics of physical world. We introduce Physical-Time Flow (PT-Flow), a novel approach that learns a continuous latent velocity field operating in physical time. Crucially, the underlying dynamics of sequential data are parameterized by an ordinary differential equation (ODE) embedded in a well-structured representation space. Under this paradigm, the prediction of future can be recast as temporal integration via an ODE solver in the compressed latent space. Building upon PT-Flow, we construct ODEWorld, a continuous-time latent world model that is both efficient and versatile. By extracting time-variant features and enforcing ODE properties on both the dynamical representation space and the latent velocity field, ODEWorld effectively addresses the long-standing representation collapse issue in latent world model literature. This also enables high-quality image reconstruction even after long-horizon prediction. Moreover, its continuous nature allows for arbitrary temporal resolution and even backward prediction, which is impossible for most discrete-time models. Lastly, ODEWorld can provide rich planning-oriented information to facilitate downstream policy learning. Comprehensive experiments demonstrate that ODEWorld successfully reconciles planning-conducive dynamics abstraction with visual realism, excelling in both video generation and robotic control. Project page: https://dstate.github.io/odeworld_website/.
Action supervision in vision-language-action (VLA) models is often treated as a downstream objective for learning action prediction. In this paper, we study it instead as a force that shapes inherited multimodal representations. We show that this shaping has a dual effect: it is necessary for forming action-compatible representations, but when action supervision is applied too directly to the inherited multimodal pathway, it can also destabilize representations that support language-side processing and object grounding. To address this tension, we introduce Action QFormer, a query-based action-facing interface that uses instruction-conditioned queries to reorganize inherited multimodal information into action-facing representations before downstream action generation. In zero-shot sim-to-real navigation, Action QFormer improves average closed-loop task success from 18.8% to 56.3%, raises fixed-instruction action-generation correctness from 22.5% to 75.5%, and nearly eliminates out-of-distribution instruction generations. Further analyses show that Action QFormer changes how action supervision shapes inherited multimodal representations, reducing broad upstream rewriting while preserving targeted and sometimes constructive action-supervised adaptation. These results suggest that improving VLA performance requires not only stronger pretrained backbones, but also better ways of selecting and organizing inherited multimodal information while controlling how it is shaped under action supervision.
Yufeng Ji, Wenhao Tang, Haoyi Niu et al.· 0 citations
Humanoid robots responding to emergency stop commands typically execute a fixed maneuver, without reasoning about whether a safe stop is actually feasible from the current state. We cast emergency stopping as a reach-avoid problem and propose Safe-Stop, a task-agnostic framework that pairs a learned stop policy with learned stoppability estimators. The estimators are complementary: a stop-probability estimator supervised by the actual outcomes of the fixed stop policy, and a reach-avoidance estimator supervised by a Hamilton-Jacobi backup over physical state. The first captures emergent stopping behavior of the learned controller; the second provides a complementary recoverability signal. Because the stop policy and estimators do not depend on the behavior policy that preceded the stop command, they transfer across diverse upstream tasks without retraining. At deployment, the two estimates are combined: Safe-Stop commits to the stop only when both estimators indicate that stopping remains feasible, otherwise it hands off to a fall policy, instantiated as a damping fallback. This agreement check yields decisions that are robust without sacrificing reactivity.
Junfeng Long, Pieter Abbeel, K. Sreenath et al.· 0 citations
We introduce trajectory-regularized stochastic optimal control (TRSOC), which augments standard stochastic optimal control (SOC) with a Kullback--Leibler (KL) divergence between controlled and reference trajectory distributions. Using Girsanov's theorem, the trajectory KL reduces to a quadratic drift mismatch penalty, yielding a modified running cost that preserves the dynamic programming (DP) structure. We derive the corresponding Hamilton--Jacobi--Bellman (HJB) equation and characterize the optimal policy. In the linear-quadratic (LQ) setting, the formulation admits a closed-form solution with an augmented control cost. Experiments show that the regularization parameter induces a trade-off between performance-driven and reference-preserving behavior, including cases with reference dynamics learned from offline data.
This survey positions humanoid control at a turning point, converging toward a unified paradigm of physics-guided generative intelligence that integrates optimization, learning, and predictive reasoning.
Yan Gu, Guanya Shi, Fan Shi et al.· Science Robotics· 7 citations
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