NebulaVLA: A Dual-Frequency Vision-Language-Action Model With Guide Action for Robotic Manipulation

Real-world deployment of Vision-Language-Action (VLA) models is often bottlenecked by efficiency-performance trade-offs, cross-embodiment generalization, and execution smoothness. We present NebulaVLA, an asynchronous dual-frequency architecture that decouples high-level semantic reasoning from low-level action control, optimizing computational resources and modularity. To bridge semantic gaps across heterogeneous robots, we introduce GESTURE-7, a unified language-grounded action representation. Furthermore, our Guide Action algorithm enforces kinematic continuity via mask-based smoothness constraints. Comprehensive evaluations demonstrate that NebulaVLA significantly outperforms synchronous baselines, achieving an 85.5\% average success rate on LIBERO-Plus and accelerating action generation by \textasciitilde 2.7$\times$. This asynchronous design enables highly efficient and responsive control for practical robotics.

Geometric Stratification for Singular Configurations of the P3P Problem via Local Dual Space

This paper investigates singular configurations of the P3P problem. Using local dual space, a systematic algebraic-computational framework is proposed to give a complete geometric stratification for the P3P singular configurations with respect to the multiplicity $μ$ of the camera center $O$: for $μ\ge 2$, $O$ lies on the ``danger cylinder'', for $μ\ge 3$, $O$ lies on one of three generatrices of the danger cylinder associated with the first Morley triangle or the circumcircle, and for $μ\ge 4$, $O$ lies on the circumcircle which indeed corresponds to infinite P3P solutions. Furthermore, a geometric stratification for the complementary configuration $O^\prime$ associated with a singular configuration $O$ is studied as well: for $μ\ge 2$, $O^\prime$ lies on a deltoidal surface associated with the danger cylinder, and for $μ\ge 3$, $O^\prime$ lies on one of three cuspidal curves of the deltoidal surface.