PolyFlow: Safe and Efficient Polytope-Constrained Flow Matching with Constraint Embedding and Projection-free Update

While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements. Existing approaches typically enforce safety through post-hoc corrections, which incur substantial computational overhead and may distort the learned distribution. We propose PolyFlow, a polytope-constrained flow matching framework that embeds constraints directly into the model and flow dynamics. PolyFlow introduces a discrete-time flow formulation and a projection-free architecture, which eliminate the discretization error and guarantee strict satisfaction of arbitrary polyhedral constraints, without the need for expensive iterative solvers. Experimental results show that PolyFlow achieves zero constraint violation while maintaining high distributional fidelity across a range of planning and control tasks. Compared to state-of-the-art constrained generation baselines, PolyFlow significantly reduces inference latency and demonstrates a favorable trade-off between safety, efficiency, and generative quality. Code is available on https://github.com/MJianM/PolyFlow.

GeoAlign: Beyond Semantics with State-Guided Spatial Alignment in VLA Models

Current Vision--Language--Action (VLA) models often optimize for semantic grounding, whereas executable manipulation requires geometry-aware spatial alignment and dynamic affordance selection. We introduce GeoAlign, a state-guided spatial alignment architecture for VLA policy learning. GeoAlign post-trains an RGB geometry branch with robot-domain RGB-D supervision, yielding RGB-derived Geometry-Enhanced Post-Trained (GEP) features for policy rollout. The robot's proprioceptive state queries the GEP feature grid, producing compact, phase-dependent geometry tokens for action prediction. GeoAlign achieves 99.0% on LIBERO, 85.3% across three SimplerEnv-Fractal tasks, and 78.8% on eight geometry-critical real-world ALOHA tasks, with ablations confirming the value of geometry post-training and proprioceptive-state-guided querying.

Global-Local Attention Decomposition for Terrain Encoding in Humanoid Perceptive Locomotion

Although reinforcement learning has significantly advanced humanoid locomotion, perceptive policies still struggle on sparse-foothold terrain and constrained environments. Success in these scenarios requires both broad terrain awareness and precise foothold selection, two perceptual roles that conventional encoders often entangle. To address this challenge, we propose Global-Local Attention Decomposition (GLAD) for terrain encoding in humanoid locomotion. Realized by a coarse-to-fine encoder over a robot-centric elevation map, GLAD explicitly separates these objectives: a global attention branch utilizes attention pooling to summarize the surrounding terrain context, while a state-conditioned local attention branch sparsifies and encodes precise foothold-relevant geometry. This explicit attention decomposition prevents the dilution of fine-grained spatial cues while reducing training overhead. Experiments demonstrate that GLAD enables reliable locomotion over challenging gaps, stepping stones, and stairs. Furthermore, the learned policy exhibits emergent terrain-responsive behaviors, autonomously following narrow paths and avoiding obstacles under simple velocity commands without explicit navigation planners. In real-world deployment on a Unitree G1 humanoid robot using onboard LiDAR, the proposed method achieves robust zero-shot sim-to-real transfer across diverse sparse-foothold and obstacle-rich domains.

HierKick: Hierarchical Reinforcement Learning for Vision-Guided Soccer Robot Control

Controlling soccer robots involves multi-time-scale decision-making, which requires balancing long-term tactical planning and short-term motion execution. Traditional end-to-end reinforcement learning (RL) methods face challenges in complex dynamic environments. This paper proposes HierKick, a vision-guided soccer robot control framework based on dual-frequency hierarchical RL. The framework adopts a hierarchical control architecture featuring a 5 Hz high-level policy that integrates YOLOv8 for real-time detection and selects tasks via a coach model, and a pre-trained 50 Hz low-level controller for precise joint control. Through this architecture, the framework achieves the four steps of approaching, aligning, dribbling, and kicking. Experimental results show that the success rates of this framework are 95.2\% in IsaacGym, 89.8\% in Mujoco, and 80\% in the real world. HierKick provides an effective hierarchical paradigm for robot control in complex environments, extendable to multi-time-scale tasks, with its modular design and skill reuse offering a new path for intelligent robot control.

HiWET: Hierarchical World-Frame End-Effector Tracking for Long-Horizon Humanoid Loco-Manipulation

Humanoid loco-manipulation requires executing precise manipulation tasks while maintaining dynamic stability amid base motion and impacts. Existing approaches typically formulate commands in body-centric frames, fail to inherently correct cumulative world-frame drift induced by legged locomotion. We reformulate the problem as world-frame end-effector tracking and propose HiWET, a hierarchical reinforcement learning framework that decouples global reasoning from dynamic execution. The high-level policy generates subgoals that jointly optimize end-effector accuracy and base positioning in the world frame, while the low-level policy executes these commands under stability constraints. We introduce a Kinematic Manifold Prior (KMP) that embeds the manipulation manifold into the action space via residual learning, reducing exploration dimensionality and mitigating kinematically invalid behaviors. Extensive simulation and ablation studies demonstrate that HiWET achieves precise and stable end-effector tracking in long-horizon world-frame tasks. We validate zero-shot sim-to-real transfer of the low-level policy on a physical humanoid, demonstrating stable locomotion under diverse manipulation commands. These results indicate that explicit world-frame reasoning combined with hierarchical control provides an effective and scalable solution for long-horizon humanoid loco-manipulation.

FocusNav: Spatial Selective Attention with Waypoint Guidance for Humanoid Local Navigation

Robust local navigation in unstructured and dynamic environments remains a significant challenge for humanoid robots, requiring a delicate balance between long-range navigation targets and immediate motion stability. In this paper, we propose FocusNav, a spatial selective attention framework that adaptively modulates the robot's perceptual field based on navigational intent and real-time stability. FocusNav features a Waypoint-Guided Spatial Cross-Attention (WGSCA) mechanism that anchors environmental feature aggregation to a sequence of predicted collision-free waypoints, ensuring task-relevant perception along the planned trajectory. To enhance robustness in complex terrains, the Stability-Aware Selective Gating (SASG) module autonomously truncates distal information when detecting instability, compelling the policy to prioritize immediate foothold safety. Extensive experiments on the Unitree G1 humanoid robot demonstrate that FocusNav significantly improves navigation success rates in challenging scenarios, outperforming baselines in both collision avoidance and motion stability, achieving robust navigation in dynamic and complex environments.