RelAfford6D: Relational 6D Affordance Graphs for Constraint-Driven Robotic Manipulation

Bridging abstract semantics and precise physical control remains a fundamental challenge in open-world robotic manipulation. While recent data-driven policies show promise, their reliance on isolated contact points or latent affordance embeddings lacks the rigorous kinematic constraints necessary for complex articulated objects.To overcome the limitation, we introduce RelAfford6D, a novel training-free framework centered on a Relational 6D Affordance Graph. Given a free-form instruction, our system deduces a semantic topology linking a primary interacting part to its physical anchor. By elevating these topological nodes into precise metric $SE(3)$ poses via vision foundation models, we analytically formulate downstream execution as a kinematic constraint satisfaction problem. The robot synthesizes continuous trajectories by tracking strictly defined physical manifolds (e.g., revolute or prismatic orbits). Coupled with a closed-loop tracking mechanism for dynamic replanning against disturbances, our physically grounded approach achieves superior zero-shot success rates, cross-category generalization and execution robustness in both simulation and the real world environments, outperforming existing data-driven baselines.

Executable Analytic Concepts as the Missing Link Between VLM Insight and Precise Manipulation

Enabling robots to perform precise and generalized manipulation in unstructured environments remains a fundamental challenge in embodied AI. While Vision-Language Models (VLMs) have demonstrated remarkable capabilities in semantic reasoning and task planning, a significant gap persists between their high-level understanding and the precise physical execution required for real-world manipulation. To bridge this "semantic-to-physical" gap, we introduce GRACE, a novel framework that grounds VLM-based reasoning through executable analytic concepts (EAC)-mathematically defined blueprints that encode object affordances, geometric constraints, and semantics of manipulation. Our approach integrates a structured policy scaffolding pipeline that turn natural language instructions and visual information into an instantiated EAC, from which we derive grasp poses, force directions and plan physically feasible motion trajectory for robot execution. GRACE thus provides a unified and interpretable interface between high-level instruction understanding and low-level robot control, effectively enabling precise and generalizable manipulation through semantic-physical grounding. Extensive experiments demonstrate that GRACE achieves strong zero-shot generalization across a variety of articulated objects in both simulated and real-world environments, without requiring task-specific training.

Differentiable Gaussian Representation for Incomplete CT Reconstruction

Incomplete Computed Tomography (CT) benefits patients by reducing radiation exposure. However, reconstructing high-fidelity images from limited views or angles remains challenging due to the ill-posed nature of the problem. Deep Learning Reconstruction (DLR) methods have shown promise in enhancing image quality, but the paradox between training data diversity and high generalization ability remains unsolved. In this paper, we propose a novel Gaussian Representation for Incomplete CT Reconstruction (GRCT) without the usage of any neural networks or full-dose CT data. Specifically, we model the 3D volume as a set of learnable Gaussians, which are optimized directly from the incomplete sinogram. Our method can be applied to multiple views and angles without changing the architecture. Additionally, we propose a differentiable Fast CT Reconstruction method for efficient clinical usage. Extensive experiments on multiple datasets and settings demonstrate significant improvements in reconstruction quality metrics and high efficiency. We plan to release our code as open-source.