Learning to Assemble Novel Structures with Unfamiliar Parts under Semantic Constraints

Multi-pair robotic assembly in unstructured environments faces spatial interference and contact uncertainties. Existing paradigms fail to bridge cognitive decision-making and physical execution, as they either encounter state-space explosion and knowledge bottlenecks or suffer from logical hallucinations and topological conflicts. We propose an end-to-end neuro-symbolic framework that solves the challenge hierarchically: generating optimal subgraphs for each pair, decoupling generality from edge cases, and then resolving cross-pair interferences. Given an eye-on-hand RGB-D assembly scene, the framework extracts semantic instance identity and state while quantifying the scene for divergence calculation. For each pair, optimal subgraph is generated via LLM using barely basic actions to mitigate hallucinations. Supportive actions for edge cases are reasoned and inserted with a lightweight discriminator. Driven by the divergence between the quantified baseline and current scene, it is easily extensible at low cost. Augmented subgraphs are topologically coordinated into global sequences while preserving internal behavioral coherence. Dynamic behavior trees embedding atomic skills close the force-aware execution loop. Offline evaluation on 100 real-world scenes achieves 97.00% global executability, outperforming classical and state-of-the-art planners. Real-robot deployment on a UR3 arm attains 90% success rate with 0.5 mm tolerance under strong interference, demonstrating a unified and verifiable solution for complex autonomous assembly.

Learning user-defined concepts as constraint networks has been extensively studied in the constraint acquisition (CA) literature. However, existing approaches typically rely on intensive interactions with a human oracle, making the learning process costly in terms of time and number of queries. In this paper, we propose a neuro-symbolic framework for automatic CA that significantly reduces user involvement by introducing neural Oracle Transformer models which learn to emulate user responses and to generalize conceptual knowledge. Trained on previously available examples, the learned oracle interacts with a dedicated CA engine, FastCA, which systematically refines the oracle's responses into a sound, consistent, and interpretable constraint network. This neuro-symbolic interaction enables the recovery of structured symbolic models from data without prior domain knowledge. Our results demonstrate that this neuro-symbolic interplay effectively aligns data-driven pattern recognition with symbolic reasoning, offering a robust approach to automating model construction in combinatorial domains.

The task of 3D assembly requires translating an understanding of parts and their relationships into precise spatial arrangements. Can pretrained general-purpose agents assemble objects through visual interaction without additional assembly-specific fine-tuning? To investigate this question, we introduce AssemblyWorld, an interactive 3D environment in which agents inspect rendered views and manipulate supplied rigid parts, guided by images or assembly manuals when available. Agents perceive part geometry through 2D views rather than direct access to mesh vertices or faces, while their resulting assemblies are evaluated geometrically. Building on this environment, we construct AssemblyWorldBench, comprising 100 assembly tasks across 80 objects spanning furniture, industrial assembly, and fracture reassembly. Evaluating eight agent systems reveals substantial differences in their capabilities. The strongest system achieves 80.9% part accuracy but 59.4% complete-assembly success. The evaluated open-source systems lag substantially behind their stronger closed-source peers in both execution reliability and assembly accuracy. Analyses of visual references, interaction trajectories, and failures show how agents revise assemblies while leaving residual positioning errors. AssemblyWorld provides a common setting for both assessing the capabilities of interactive assembly agents and characterizing the gap between approximate structure recovery and precise reconstruction.